Essec\Faculty\Model\Profile {#2216 ▼
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"bid" => "B00809923"
"academId" => "32281"
"slug" => "alquier-pierre"
"fullName" => "Pierre ALQUIER"
"lastName" => "ALQUIER"
"firstName" => "Pierre"
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]
"email" => "b00809923@essec.edu"
"status" => "ACTIF"
"campus" => "Campus de Singapour"
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"externalCvUrl" => "https://faculty.essec.edu/en/cv/alquier-pierre/pdf"
"googleScholarUrl" => "https://scholar.google.com/citations?user=ngkCAJYAAAAJ"
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"career" => array:6 [
0 => Essec\Faculty\Model\CareerItem {#2260
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]
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}
1 => Essec\Faculty\Model\CareerItem {#2261
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"fr" => "RIKEN"
"en" => "RIKEN"
]
"country" => array:2 [
"fr" => "Japon"
"en" => "Japan"
]
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}
2 => Essec\Faculty\Model\CareerItem {#2262
#_index: null
#_id: null
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]
"country" => array:2 [
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]
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}
3 => Essec\Faculty\Model\CareerItem {#2263
#_index: null
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"en" => "University College of Dublin"
]
"country" => array:2 [
"fr" => "Irlande"
"en" => "Ireland"
]
]
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}
4 => Essec\Faculty\Model\CareerItem {#2264
#_index: null
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5 => Essec\Faculty\Model\CareerItem {#2265
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"diplomes" => array:4 [
0 => Essec\Faculty\Model\Diplome {#2218
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1 => Essec\Faculty\Model\Diplome {#2220
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2 => Essec\Faculty\Model\Diplome {#2217
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3 => Essec\Faculty\Model\Diplome {#2221
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"bio" => array:2 [
"fr" => null
"en" => """
<p>Pierre Alquier is a Professor at ESSEC Business School, in the Department of Information Systems, Data Analytics and Operations (IDO), since January 2023.</p>\n 
<p>Pierre Alquier is a Professor at ESSEC Business School, in the Department of Information Systems,
\n
<p>At ESSEC, he teaches introductory classes on statistics, data science and machine learning with Python and R, in various programs: BBA, Master in Finance, Master SMIB (Strategy and Management of International Business). He also teaches an advanced class on online learning and optimization for the ESSEC-Centrale-Supelec Master in Data Science and Business Analytics.</p>\n <p>At ESSEC, he teaches introductory classes on statistics, data science and machine learning with P
\n
<p>His research focuses on the statistical and theoretical aspects of machine learning in general, with special focus on approximate Bayesian methods, high-dimensional models, robust learning and learning with dependent observations. He published a monograph on statistical learning theory with PAC-Bayes bounds: <a href="https://doi.org/10.1561/2200000100">User-friendly introduction to PAC-Bayes bounds</a>, and edited a textbook on high-dimensional models in statistics and econometrics: <a href="http://dx.doi.org/10.1007/978-3-642-19989-9">Inverse Problems and High-Dimensional Estimation</a>.</p>\n <p>His research focuses on the statistical and theoretical aspects of machine learning in general, w
\n
<p>Pierre Alquier serves as an Action Editor for the <a href="https://www.jmlr.org/">Journal of Machine Learning Research</a> and an Associate Editor for the <a href="https://imstat.org/journals-and-publications/electronic-journal-of-statistics/">Electronic Journal of Statistics</a>. He is a member of the <a href="http://algorithmiclearningtheory.org/alt-steering-committee/">ALT Steering Committee</a> in charge of the organization of the conference on Algorithmic Learning Theory (ALT) since 1990. He also served as an Action Editor for Transactions in Machine Learning Research, as a Senior Area Chair for ICML and as an Area Chair or Program Chair for major machine learning conferences such as ACML, AISTATS, ALT, COLT and NeurIPS.</p>\n <p>Pierre Alquier serves as an Action Editor for the <a href="https://www.jmlr.org/">Journal of Mach
\n
<p>Pierre holds a PhD from Sorbonne University, an M. Sc. in probability from Sorbonne University and a degree in statistics and econometrics from ENSAE Paris. Before joining ESSEC, he was a <i>maître de conférences</i> (assistant professor) at Paris Cité University, a lecturer at UCD Dublin, a Professor at ENSAE Paris and a research scientist at the Center for Advanced Intelligence Project of RIKEN, in Tokyo.</p>\n <p>Pierre holds a PhD from Sorbonne University, an M. Sc. in probability from Sorbonne University an
"""
]
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"distinctions" => array:1 [
0 => Essec\Faculty\Model\Distinction {#2266
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"date" => "2019-11-17"
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"tri" => " 1 "
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"en" => "Japan"
]
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0 => Essec\Faculty\Model\TeachingItem {#2255
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Quelques contributions à la statistique des modèles dynamiques\n
aléatoires
"""
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Quelques contributions à la statistique des modèles dynamiques\n
aléatoires
"""
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"country" => array:2 [
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1 => Essec\Faculty\Model\TeachingItem {#2256
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2 => Essec\Faculty\Model\TeachingItem {#2257
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3 => Essec\Faculty\Model\TeachingItem {#2258
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4 => Essec\Faculty\Model\TeachingItem {#2259
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"institution" => array:2 [
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"en" => "Central Michigan University"
]
"country" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
]
+lang: "en"
+"parent": Essec\Faculty\Model\Profile {#2216}
}
33 => Essec\Faculty\Model\ExtraActivity {#2253
#_index: null
#_id: null
#_source: array:9 [
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"type" => array:2 [
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"en" => "Participation in scientific commissions or reviewer for a conference"
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"fr" => "Université Mohammed V"
"en" => "Université Mohammed V"
]
"country" => array:2 [
"fr" => "Maroc"
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]
]
+lang: "en"
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}
34 => Essec\Faculty\Model\ExtraActivity {#2254
#_index: null
#_id: null
#_source: array:9 [
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"en" => "Association for Algorithmic Learning Theory (AALT)"
]
"country" => array:2 [
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]
]
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}
]
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0 => Essec\Faculty\Model\These {#2267
#_index: null
#_id: null
#_source: array:9 [
"year" => "2019"
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"student" => "CAREL L."
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"label" => array:2 [
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"en" => "Big data analysis in the field of transportation"
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"role" => array:2 [
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"en" => "Thesis director"
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]
"country" => array:2 [
"fr" => "France"
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]
]
+lang: "en"
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}
1 => Essec\Faculty\Model\These {#2268
#_index: null
#_id: null
#_source: array:9 [
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"student" => "CHÉRIEF-ABDELLATIF B.-E."
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"label" => array:2 [
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"role" => array:2 [
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"en" => "L'École nationale de la statistique et de l'administration économique (ENSAE)"
]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "en"
+"parent": Essec\Faculty\Model\Profile {#2216}
}
2 => Essec\Faculty\Model\These {#2269
#_index: null
#_id: null
#_source: array:9 [
"year" => "2017"
"startDate" => null
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"student" => "COTTET V."
"firstJob" => "Senior statistician, INSEE"
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"role" => array:2 [
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]
"country" => array:2 [
"fr" => "France"
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]
]
+lang: "en"
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}
3 => Essec\Faculty\Model\These {#2270
#_index: null
#_id: null
#_source: array:9 [
"year" => "2017"
"startDate" => null
"endDate" => "2017"
"student" => "MAI T. T."
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]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "en"
+"parent": Essec\Faculty\Model\Profile {#2216}
}
4 => Essec\Faculty\Model\These {#2271
#_index: null
#_id: null
#_source: array:9 [
"year" => "2023"
"startDate" => null
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"student" => "ROSIER A."
"firstJob" => "Enseignant-chercheur à l'école d'ingénieurs ESME"
"label" => array:2 [
"fr" => """
Quelques contributions à la statistique des modèles dynamiques\n
aléatoires
"""
"en" => "Contributions to statistics of stochastic processes"
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"role" => array:2 [
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"institution" => array:2 [
"fr" => "Université Paris X Nanterre"
"en" => "Université Paris X Nanterre"
]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "en"
+"parent": Essec\Faculty\Model\Profile {#2216}
}
]
"sitePerso" => "https://pierrealquier.github.io/"
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0 => Essec\Faculty\Model\Contribution {#2273
#_index: "academ_contributions"
#_id: "14429"
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"slug" => "14429-fast-rates-in-meta-learning-with-pac-bayes-bounds"
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"year" => "2023"
"title" => "Fast Rates in Meta-Learning with PAC-Bayes Bounds"
"description" => "ALQUIER, P. et CHÉRIEF-ABDELLATIF, B.E. (2023). Fast Rates in Meta-Learning with PAC-Bayes Bounds. Dans: 12th Workshop on High Dimensional Data Analysis 2023. Rabat. ALQUIER, P. et CHÉRIEF-ABDELLATIF, B.E. (2023). Fast Rates in Meta-Learning with PAC-Bayes Bounds. D "
"authors" => array:2 [
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1 => array:1 [
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"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
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}
1 => Essec\Faculty\Model\Contribution {#2275
#_index: "academ_contributions"
#_id: "14433"
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"id" => "14433"
"slug" => "14433-getting-organised-for-ai"
"yearMonth" => "2023-09"
"year" => "2023"
"title" => "Getting organised for AI"
"description" => "ALQUIER, P. 2023. <i>Getting organised for AI</i>. Septembre."
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
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"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://www.theedgesingapore.com/digitaledge/cxos/getting-organised-ai"
"publicationInfo" => array:3 [
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"type" => array:2 [
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"support_type" => array:2 [
"fr" => "Presse"
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"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
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}
2 => Essec\Faculty\Model\Contribution {#2277
#_index: "academ_contributions"
#_id: "14602"
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"slug" => "14602-a-i-an-enabler-not-a-solution"
"yearMonth" => "2023-10"
"year" => "2023"
"title" => "A.I. -- An Enabler, Not A Solution"
"description" => "ALQUIER, P. 2023. <i>A.I. -- An Enabler, Not A Solution</i>. Octobre."
"authors" => array:1 [
0 => array:3 [
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"bid" => "B00809923"
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"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://storm-asia.com/wedwebchat-ai-enabler-not-a-solution/"
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"type" => array:2 [
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"countries" => array:2 [
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"abstract" => array:2 [
"fr" => null
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"authors_fields" => array:2 [
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"en" => "Information Systems, Data Analytics and Operations"
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"indexedAt" => "2025-04-02T19:21:40.000Z"
]
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}
3 => Essec\Faculty\Model\Contribution {#2274
#_index: "academ_contributions"
#_id: "14732"
#_source: array:18 [
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"slug" => "14732-concentration-of-variational-approximations"
"yearMonth" => "2023-04"
"year" => "2023"
"title" => "Concentration of variational approximations"
"description" => "ALQUIER, P. (2023). Concentration of variational approximations. Dans: Department of Statistics and Data Science Seminar. Singapore. ALQUIER, P. (2023). Concentration of variational approximations. Dans: Department of Statistics and "
"authors" => array:1 [
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"fr" => null
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"authors_fields" => array:2 [
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"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
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}
4 => Essec\Faculty\Model\Contribution {#2278
#_index: "academ_contributions"
#_id: "14733"
#_source: array:18 [
"id" => "14733"
"slug" => "14733-robust-estimation-with-mmd"
"yearMonth" => "2023-11"
"year" => "2023"
"title" => "Robust estimation with MMD"
"description" => "ALQUIER, P. (2023). Robust estimation with MMD. Dans: UCD School of Mathematics and Statistics -- Statistics Seminar. Dublin. ALQUIER, P. (2023). Robust estimation with MMD. Dans: UCD School of Mathematics and Statistics -- St "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
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"ouvrage" => "UCD School of Mathematics and Statistics -- Statistics Seminar"
"keywords" => []
"updatedAt" => "2024-03-07 17:01:51"
"publicationUrl" => null
"publicationInfo" => array:3 [
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"volume" => ""
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"type" => array:2 [
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"fr" => null
"en" => null
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"countries" => array:2 [
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"fr" => ""
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"authors_fields" => array:2 [
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"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
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+"parent": null
}
5 => Essec\Faculty\Model\Contribution {#2272
#_index: "academ_contributions"
#_id: "14734"
#_source: array:18 [
"id" => "14734"
"slug" => "14734-robust-estimation-and-regression-with-mmd"
"yearMonth" => "2023-12"
"year" => "2023"
"title" => "Robust estimation and regression with MMD"
"description" => "ALQUIER, P. (2023). Robust estimation and regression with MMD. Dans: Séminaire de Probabilités et Statistiques d'Orsay. Orsay. ALQUIER, P. (2023). Robust estimation and regression with MMD. Dans: Séminaire de Probabilités et St "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
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"ouvrage" => "Séminaire de Probabilités et Statistiques d'Orsay"
"keywords" => []
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"publicationUrl" => null
"publicationInfo" => array:3 [
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"support_type" => array:2 [
"fr" => null
"en" => null
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"countries" => array:2 [
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"abstract" => array:2 [
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"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
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}
6 => Essec\Faculty\Model\Contribution {#2276
#_index: "academ_contributions"
#_id: "14735"
#_source: array:18 [
"id" => "14735"
"slug" => "14735-rates-of-convergence-in-bayesian-meta-learning"
"yearMonth" => "2023-12"
"year" => "2023"
"title" => "Rates of convergence in Bayesian meta-learning"
"description" => "ALQUIER, P. (2023). Rates of convergence in Bayesian meta-learning. Dans: UCL Statistical Science Seminars. London. ALQUIER, P. (2023). Rates of convergence in Bayesian meta-learning. Dans: UCL Statistical Science Se "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
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]
"ouvrage" => "UCL Statistical Science Seminars"
"keywords" => []
"updatedAt" => "2025-02-13 16:49:08"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Présentations dans un séminaire de recherche"
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"support_type" => array:2 [
"fr" => null
"en" => null
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"countries" => array:2 [
"fr" => null
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"abstract" => array:2 [
"fr" => ""
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]
"authors_fields" => array:2 [
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"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
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+"parent": null
}
7 => Essec\Faculty\Model\Contribution {#2279
#_index: "academ_contributions"
#_id: "14736"
#_source: array:18 [
"id" => "14736"
"slug" => "14736-robust-estimation-and-regression-with-mmd"
"yearMonth" => "2023-12"
"year" => "2023"
"title" => "Robust estimation and regression with MMD"
"description" => "ALQUIER, P. (2023). Robust estimation and regression with MMD. Dans: Séminaire de Statistique du Laboratoire "Probabilités, Statistiques et Modélisation". Paris. ALQUIER, P. (2023). Robust estimation and regression with MMD. Dans: Séminaire de Statistique du Lab "
"authors" => array:1 [
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"ouvrage" => "Séminaire de Statistique du Laboratoire "Probabilités, Statistiques et Modélisation""
"keywords" => []
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"en" => "Information Systems, Data Analytics and Operations"
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"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
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}
8 => Essec\Faculty\Model\Contribution {#2280
#_index: "academ_contributions"
#_id: "14796"
#_source: array:18 [
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"slug" => "14796-pac-bayes-bounds-understanding-the-generalization-of-bayesian-learning-algorithms"
"yearMonth" => "2024-06"
"year" => "2024"
"title" => "PAC-Bayes bounds: understanding the generalization of Bayesian learning algorithms"
"description" => "ALQUIER, P. (2024). PAC-Bayes bounds: understanding the generalization of Bayesian learning algorithms. Dans: CNRS - ESSEC APAC Workshop. Singapore. ALQUIER, P. (2024). PAC-Bayes bounds: understanding the generalization of Bayesian learning algorit "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
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]
"ouvrage" => "CNRS - ESSEC APAC Workshop"
"keywords" => []
"updatedAt" => "2024-06-11 07:15:22"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
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]
"type" => array:2 [
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"en" => "Presentations at an Academic or Professional conference"
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"support_type" => array:2 [
"fr" => null
"en" => null
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"countries" => array:2 [
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"authors_fields" => array:2 [
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"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
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}
9 => Essec\Faculty\Model\Contribution {#2281
#_index: "academ_contributions"
#_id: "14797"
#_source: array:18 [
"id" => "14797"
"slug" => "14797-pac-bayesian-bounds-for-offline-contextual-bandits"
"yearMonth" => "2024-05"
"year" => "2024"
"title" => "PAC-Bayesian Bounds for Offline Contextual Bandits"
"description" => "ALQUIER, P. (2024). PAC-Bayesian Bounds for Offline Contextual Bandits. Dans: Mini-Workshop on Learning Theory & Methodology at NTU. Singapore. ALQUIER, P. (2024). PAC-Bayesian Bounds for Offline Contextual Bandits. Dans: Mini-Workshop on Learn "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "Mini-Workshop on Learning Theory & Methodology at NTU"
"keywords" => []
"updatedAt" => "2024-05-28 10:00:31"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
10 => Essec\Faculty\Model\Contribution {#2282
#_index: "academ_contributions"
#_id: "14838"
#_source: array:18 [
"id" => "14838"
"slug" => "14838-learning-with-pac-bayes-bounds"
"yearMonth" => "2024-06"
"year" => "2024"
"title" => "Learning with PAC-Bayes bounds"
"description" => "ALQUIER, P. (2024). Learning with PAC-Bayes bounds. Dans: Third RIKEN AIP & A*STAR-CFAR Joint Workshop on Machine Learning and Artificial Intelligence. Singapore. ALQUIER, P. (2024). Learning with PAC-Bayes bounds. Dans: Third RIKEN AIP & A*STAR-CFAR Joint Worksh "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "Third RIKEN AIP & A*STAR-CFAR Joint Workshop on Machine Learning and Artificial Intelligence"
"keywords" => []
"updatedAt" => "2024-06-24 13:46:19"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
11 => Essec\Faculty\Model\Contribution {#2283
#_index: "academ_contributions"
#_id: "15028"
#_source: array:18 [
"id" => "15028"
"slug" => "15028-optimistic-estimation-of-convergence-in-markov-chains-with-the-average-mixing-time"
"yearMonth" => "2024-12"
"year" => "2024"
"title" => "Optimistic Estimation of Convergence in Markov Chains with the Average Mixing Time"
"description" => "WOLFER, G. et ALQUIER, P. (2024). Optimistic Estimation of Convergence in Markov Chains with the Average Mixing Time. Dans: DeLTA Lab seminar, University of Copenhagen. Copenhagen. WOLFER, G. et ALQUIER, P. (2024). Optimistic Estimation of Convergence in Markov Chains with the Ave "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "WOLFER Geoffrey"
]
]
"ouvrage" => "DeLTA Lab seminar, University of Copenhagen"
"keywords" => []
"updatedAt" => "2024-12-09 11:20:45"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Présentations dans un séminaire de recherche"
"en" => "Presentations at a Faculty research seminar"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
12 => Essec\Faculty\Model\Contribution {#2284
#_index: "academ_contributions"
#_id: "15031"
#_source: array:18 [
"id" => "15031"
"slug" => "15031-optimistic-estimation-of-convergence-in-markov-chains-with-the-average-mixing-time"
"yearMonth" => "2024-12"
"year" => "2024"
"title" => "Optimistic Estimation of Convergence in Markov Chains with the Average Mixing Time"
"description" => "WOLFER, G. et ALQUIER, P. (2024). Optimistic Estimation of Convergence in Markov Chains with the Average Mixing Time. Dans: Meeting in Mathematical Statistics, CIRM. Marseille. WOLFER, G. et ALQUIER, P. (2024). Optimistic Estimation of Convergence in Markov Chains with the Ave "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "WOLFER Geoffrey"
]
]
"ouvrage" => "Meeting in Mathematical Statistics, CIRM"
"keywords" => []
"updatedAt" => "2024-12-18 16:47:03"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
13 => Essec\Faculty\Model\Contribution {#2285
#_index: "academ_contributions"
#_id: "15325"
#_source: array:18 [
"id" => "15325"
"slug" => "15325-laplace-vs-variational-approximations-a-biased-point-of-view"
"yearMonth" => "2024-11"
"year" => "2024"
"title" => "Laplace vs. variational approximations: a biased point of view"
"description" => "ALQUIER, P. (2024). Laplace vs. variational approximations: a biased point of view. Dans: Rethinking the Role of Bayesianism in the Age of Modern AI, Dagstuhl Seminar 24461. Dagstuhl. ALQUIER, P. (2024). Laplace vs. variational approximations: a biased point of view. Dans: Rethinking "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "Rethinking the Role of Bayesianism in the Age of Modern AI, Dagstuhl Seminar 24461"
"keywords" => []
"updatedAt" => "2024-11-25 11:06:04"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
14 => Essec\Faculty\Model\Contribution {#2286
#_index: "academ_contributions"
#_id: "13863"
#_source: array:18 [
"id" => "13863"
"slug" => "13863-chatgpt"
"yearMonth" => "2023-03"
"year" => "2023"
"title" => "ChatGPT"
"description" => "ALQUIER, P. 2023. <i>ChatGPT</i>. Mars."
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-21 09:57:42"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Interviews : Emission radio - TV - presse écrite"
"en" => "Interviews: radio - TV - press"
]
"support_type" => array:2 [
"fr" => "Presse"
"en" => "Press"
]
"countries" => array:2 [
"fr" => "Singapour"
"en" => "Singapore"
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
15 => Essec\Faculty\Model\Contribution {#2287
#_index: "academ_contributions"
#_id: "13883"
#_source: array:18 [
"id" => "13883"
"slug" => "13883-inverse-problems-and-high-dimensional-estimation"
"yearMonth" => "2011-06"
"year" => "2011"
"title" => "Inverse Problems and High-Dimensional Estimation"
"description" => "ALQUIER, P., GAUTIER, E. et STOLTZ, G. [Eds] (2011). <i>Inverse Problems and High-Dimensional Estimation</i>. Springer Berlin Heidelberg. ALQUIER, P., GAUTIER, E. et STOLTZ, G. [Eds] (2011). <i>Inverse Problems and High-Dimensional Estima "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "GAUTIER Eric"
]
2 => array:1 [
"name" => "STOLTZ Gilles"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 13:44:09"
"publicationUrl" => "https://link.springer.com/book/10.1007/978-3-642-19989-9"
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Direction d'ouvrage"
"en" => "Book editor"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
16 => Essec\Faculty\Model\Contribution {#2288
#_index: "academ_contributions"
#_id: "13888"
#_source: array:18 [
"id" => "13888"
"slug" => "13888-generative-ai-friend-or-foe"
"yearMonth" => "2023-03"
"year" => "2023"
"title" => "Generative AI: Friend or Foe?"
"description" => "ALQUIER, P. 2023. <i>Generative AI: Friend or Foe?</i> Mars."
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://www.theedgesingapore.com/digitaledge/focus/generative-ai-friend-or-foe"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Interviews : Emission radio - TV - presse écrite"
"en" => "Interviews: radio - TV - press"
]
"support_type" => array:2 [
"fr" => "Presse"
"en" => "Press"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Comments with Nurdianah Md Nur"
"en" => "Comments with Nurdianah Md Nur"
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
17 => Essec\Faculty\Model\Contribution {#2289
#_index: "academ_contributions"
#_id: "14355"
#_source: array:18 [
"id" => "14355"
"slug" => "14355-rates-of-convergence-in-bayesian-meta-learning"
"yearMonth" => "2024-01"
"year" => "2024"
"title" => "Rates of Convergence in Bayesian Meta-learning"
"description" => "ALQUIER, P., RIOU, C. et CHÉRIEF-ABDELLATIF, B.E. (2024). Rates of Convergence in Bayesian Meta-learning. Dans: 2024 IMS Asia-Pacific Rim Meeting. Melbourne. ALQUIER, P., RIOU, C. et CHÉRIEF-ABDELLATIF, B.E. (2024). Rates of Convergence in Bayesian Meta-lear "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "RIOU Charles"
]
2 => array:1 [
"name" => "CHÉRIEF-ABDELLATIF Badr-Eddine"
]
]
"ouvrage" => "2024 IMS Asia-Pacific Rim Meeting"
"keywords" => []
"updatedAt" => "2025-02-13 16:48:35"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
18 => Essec\Faculty\Model\Contribution {#2290
#_index: "academ_contributions"
#_id: "14378"
#_source: array:18 [
"id" => "14378"
"slug" => "14378-rates-of-convergence-in-bayesian-meta-learning"
"yearMonth" => "2023-08"
"year" => "2023"
"title" => "Rates of convergence in Bayesian meta-learning"
"description" => "ALQUIER, P., RIOU, C. et CHÉRIEF-ABDELLATIF, B.E. (2023). Rates of convergence in Bayesian meta-learning. Dans: 6th International Conference on Econometrics and Statistics 2023. Tokyo. ALQUIER, P., RIOU, C. et CHÉRIEF-ABDELLATIF, B.E. (2023). Rates of convergence in Bayesian meta-lear "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "RIOU Charles"
]
2 => array:1 [
"name" => "CHÉRIEF-ABDELLATIF Badr-Eddine"
]
]
"ouvrage" => "6th International Conference on Econometrics and Statistics 2023"
"keywords" => []
"updatedAt" => "2025-02-13 16:48:53"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
19 => Essec\Faculty\Model\Contribution {#2291
#_index: "academ_contributions"
#_id: "13864"
#_source: array:18 [
"id" => "13864"
"slug" => "13864-concentration-of-tempered-posteriors-and-of-their-variational-approximations"
"yearMonth" => "2020-06"
"year" => "2020"
"title" => "Concentration of tempered posteriors and of their variational approximations"
"description" => "ALQUIER, P. et RIDGWAY, J. (2020). Concentration of tempered posteriors and of their variational approximations. <i>Annals of Statistics</i>, 48(3), pp. 1475-1497. ALQUIER, P. et RIDGWAY, J. (2020). Concentration of tempered posteriors and of their variational app "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "RIDGWAY James"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-17 01:00:45"
"publicationUrl" => "https://doi.org/10.1214/19-AOS1855"
"publicationInfo" => array:3 [
"pages" => "1475-1497"
"volume" => "48"
"number" => "3"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => """
While Bayesian methods are extremely popular in statistics and machine\n
learning, their application to massive data sets is often challenging, when\n
possible at all. The classical MCMC algorithms are prohibitively slow when\n
both the model dimension and the sample size are large. Variational Bayesian\n
methods aim at approximating the posterior by a distribution in a tractable\n
family F. Thus, MCMC are replaced by an optimization algorithm which is\n
orders of magnitude faster. VB methods have been applied in such computationally demanding applications as collaborative filtering, image and video\n orders of magnitude faster. VB methods have been applied in such computationally demanding applicati
processing or NLP to name a few. However, despite nice results in practice,\n
the theoretical properties of these approximations are not known. We propose\n
a general oracle inequality that relates the quality of the VB approximation to\n
the prior π and to the structure of F. We provide a simple condition that allows to derive rates of convergence from this oracle inequality. We apply our\n the prior π and to the structure of F. We provide a simple condition that allows to derive rates of
theory to various examples. First, we show that for parametric models with\n
log-Lipschitz likelihood, Gaussian VB leads to efficient algorithms and consistent estimators. We then study a high-dimensional example: matrix completion, and a nonparametric example: density estimation. log-Lipschitz likelihood, Gaussian VB leads to efficient algorithms and consistent estimators. We th
"""
"en" => """
While Bayesian methods are extremely popular in statistics and machine\n
learning, their application to massive data sets is often challenging, when\n
possible at all. The classical MCMC algorithms are prohibitively slow when\n
both the model dimension and the sample size are large. Variational Bayesian\n
methods aim at approximating the posterior by a distribution in a tractable\n
family F. Thus, MCMC are replaced by an optimization algorithm which is\n
orders of magnitude faster. VB methods have been applied in such computationally demanding applications as collaborative filtering, image and video\n orders of magnitude faster. VB methods have been applied in such computationally demanding applicati
processing or NLP to name a few. However, despite nice results in practice,\n
the theoretical properties of these approximations are not known. We propose\n
a general oracle inequality that relates the quality of the VB approximation to\n
the prior π and to the structure of F. We provide a simple condition that allows to derive rates of convergence from this oracle inequality. We apply our\n the prior π and to the structure of F. We provide a simple condition that allows to derive rates of
theory to various examples. First, we show that for parametric models with\n
log-Lipschitz likelihood, Gaussian VB leads to efficient algorithms and consistent estimators. We then study a high-dimensional example: matrix completion, and a nonparametric example: density estimation. log-Lipschitz likelihood, Gaussian VB leads to efficient algorithms and consistent estimators. We th
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
20 => Essec\Faculty\Model\Contribution {#2292
#_index: "academ_contributions"
#_id: "13865"
#_source: array:18 [
"id" => "13865"
"slug" => "13865-estimation-bounds-and-sharp-oracle-inequalities-of-regularized-procedures-with-lipschitz-loss-functions 13865-estimation-bounds-and-sharp-oracle-inequalities-of-regularized-procedures-with-lipschitz-loss- "
"yearMonth" => "2019-08"
"year" => "2019"
"title" => "Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functi "
"description" => "ALQUIER, P., COTTET, V. et LECUE, G. (2019). Estimation bounds and sharp oracle inequalities of regularized procedures with Lipschitz loss functions. <i>Annals of Statistics</i>, 47(4), pp. 2117-2144. ALQUIER, P., COTTET, V. et LECUE, G. (2019). Estimation bounds and sharp oracle inequalities of regu "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:3 [
"name" => "LECUE Guillaume"
"bid" => "B00806953"
"slug" => "lecue-guillaume"
]
2 => array:1 [
"name" => "COTTET Vincent"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/18-AOS1742"
"publicationInfo" => array:3 [
"pages" => "2117-2144"
"volume" => "47"
"number" => "4"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => """
Many classification and regression problems are solved in practice by regularized empirical risk minimizers (RERM). The risk is measured\n Many classification and regression problems are solved in practice by regularized empirical risk min
via a loss function. The quadratic loss function is the most popular function for\n
regression. It has been extensively studied (cf. [23, 31] among others). Still many other loss functions are popular among practitioners and are indeed extremely useful in specific situations regression. It has been extensively studied (cf. [23, 31] among others). Still many other loss funct
"""
"en" => """
Many classification and regression problems are solved in practice by regularized empirical risk minimizers (RERM). The risk is measured\n Many classification and regression problems are solved in practice by regularized empirical risk min
via a loss function. The quadratic loss function is the most popular function for\n
regression. It has been extensively studied (cf. [23, 31] among others). Still many other loss functions are popular among practitioners and are indeed extremely useful in specific situations regression. It has been extensively studied (cf. [23, 31] among others). Still many other loss funct
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
21 => Essec\Faculty\Model\Contribution {#2293
#_index: "academ_contributions"
#_id: "13866"
#_source: array:18 [
"id" => "13866"
"slug" => "13866-consistency-of-variational-bayes-inference-for-estimation-and-model-selection-in-mixtures"
"yearMonth" => "2018-09"
"year" => "2018"
"title" => "Consistency of variational Bayes inference for estimation and model selection in mixtures"
"description" => "CHERIEF-ABDELLATIF, B.E. et ALQUIER, P. (2018). Consistency of variational Bayes inference for estimation and model selection in mixtures. <i>The Electronic Journal of Statistics</i>, 12(2), pp. 2995-3035. CHERIEF-ABDELLATIF, B.E. et ALQUIER, P. (2018). Consistency of variational Bayes inference for estim "
"authors" => array:2 [
0 => array:2 [
"name" => "CHERIEF-ABDELLATIF Badr-Eddine"
"bid" => "B00810114"
]
1 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "Mixture models"
1 => "frequentist evaluation of Bayesian methods"
2 => "variational approximations"
3 => "model selection"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/18-EJS1475"
"publicationInfo" => array:3 [
"pages" => "2995-3035"
"volume" => "12"
"number" => "2"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable posteriors thanks to optimization algorithms, is extremely popular in practice when dealing with complex models such as mixtures. The contribution of this paper is two-fold. First, we study the concentration of variational approximations of posteriors, which is still an open problem for general mixtures, and we derive consistency and rates of convergence. We also tackle the problem of model selection for the number of components: we study the approach already used in practice, which consists in maximizing a numerical criterion (the Evidence Lower Bound). We prove that this strategy indeed leads to strong oracle inequalities. We illustrate our theoretical results by applications to Gaussian and multinomial mixtures. Mixture models are widely used in Bayesian statistics and machine learning, in particular in computa "
"en" => "Mixture models are widely used in Bayesian statistics and machine learning, in particular in computational biology, natural language processing and many other fields. Variational inference, a technique for approximating intractable posteriors thanks to optimization algorithms, is extremely popular in practice when dealing with complex models such as mixtures. The contribution of this paper is two-fold. First, we study the concentration of variational approximations of posteriors, which is still an open problem for general mixtures, and we derive consistency and rates of convergence. We also tackle the problem of model selection for the number of components: we study the approach already used in practice, which consists in maximizing a numerical criterion (the Evidence Lower Bound). We prove that this strategy indeed leads to strong oracle inequalities. We illustrate our theoretical results by applications to Gaussian and multinomial mixtures. Mixture models are widely used in Bayesian statistics and machine learning, in particular in computa "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
22 => Essec\Faculty\Model\Contribution {#2294
#_index: "academ_contributions"
#_id: "13867"
#_source: array:18 [
"id" => "13867"
"slug" => "13867-simpler-pac-bayesian-bounds-for-hostile-data"
"yearMonth" => "2018-05"
"year" => "2018"
"title" => "Simpler PAC-Bayesian bounds for hostile data"
"description" => "ALQUIER, P. et GUEDJ, B. (2018). Simpler PAC-Bayesian bounds for hostile data. <i>Machine Learning</i>, 107(5), pp. 887-902. ALQUIER, P. et GUEDJ, B. (2018). Simpler PAC-Bayesian bounds for hostile data. <i>Machine Learning</ "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "GUEDJ Benjamin"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://link.springer.com/article/10.1007/s10994-017-5690-0"
"publicationInfo" => array:3 [
"pages" => "887-902"
"volume" => "107"
"number" => "5"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
"abstract" => array:2 [
"fr" => """
PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution ρ\n PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to
to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distribution π\n to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distributio
. Unfortunately, most of the available bounds typically rely on heavy assumptions such as boundedness and independence of the observations. This paper aims at relaxing these constraints and provides PAC-Bayesian learning bounds that hold for dependent, heavy-tailed observations (hereafter referred to as hostile data). In these bounds the Kullack-Leibler divergence is replaced with a general version of Csiszár’s f-divergence. We prove a general PAC-Bayesian bound, and show how to use it in various hostile settings. . Unfortunately, most of the available bounds typically rely on heavy assumptions such as boundednes
"""
"en" => """
PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to connect the generalization ability of an aggregation distribution ρ\n PAC-Bayesian learning bounds are of the utmost interest to the learning community. Their role is to
to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distribution π\n to its empirical risk and to its Kullback-Leibler divergence with respect to some prior distributio
. Unfortunately, most of the available bounds typically rely on heavy assumptions such as boundedness and independence of the observations. This paper aims at relaxing these constraints and provides PAC-Bayesian learning bounds that hold for dependent, heavy-tailed observations (hereafter referred to as hostile data). In these bounds the Kullack-Leibler divergence is replaced with a general version of Csiszár’s f-divergence. We prove a general PAC-Bayesian bound, and show how to use it in various hostile settings. . Unfortunately, most of the available bounds typically rely on heavy assumptions such as boundednes
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
23 => Essec\Faculty\Model\Contribution {#2295
#_index: "academ_contributions"
#_id: "13868"
#_source: array:18 [
"id" => "13868"
"slug" => "13868-deviation-inequalities-for-stochastic-approximation-by-averaging"
"yearMonth" => "2022-10"
"year" => "2022"
"title" => "Deviation inequalities for stochastic approximation by averaging"
"description" => "FAN, X., ALQUIER, P. et DOUKHAN, P. (2022). Deviation inequalities for stochastic approximation by averaging. <i>Stochastic Processes and their Applications</i>, 152, pp. 452-485. FAN, X., ALQUIER, P. et DOUKHAN, P. (2022). Deviation inequalities for stochastic approximation by a "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "FAN Xiequan"
]
2 => array:1 [
"name" => "DOUKHAN Paul"
]
]
"ouvrage" => ""
"keywords" => array:5 [
0 => "Deviation inequalities"
1 => "Martingales"
2 => "Iterated random functions"
3 => "Stochastic approximation by averaging"
4 => "Empirical risk minimization"
]
"updatedAt" => "2023-07-10 16:36:07"
"publicationUrl" => "https://doi.org/10.1016/j.spa.2022.07.002"
"publicationInfo" => array:3 [
"pages" => "452-485"
"volume" => "152"
"number" => ""
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We introduce a class of Markov chains that includes models of stochastic approximation by averaging and non-averaging. Using a martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences. Finally, we apply these inequalities to stochastic approximation by averaging and empirical risk minimization. We introduce a class of Markov chains that includes models of stochastic approximation by averaging "
"en" => "We introduce a class of Markov chains that includes models of stochastic approximation by averaging and non-averaging. Using a martingale approximation method, we establish various deviation inequalities for separately Lipschitz functions of such a chain, with different moment conditions on some dominating random variables of martingale differences. Finally, we apply these inequalities to stochastic approximation by averaging and empirical risk minimization. We introduce a class of Markov chains that includes models of stochastic approximation by averaging "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
24 => Essec\Faculty\Model\Contribution {#2296
#_index: "academ_contributions"
#_id: "13869"
#_source: array:18 [
"id" => "13869"
"slug" => "13869-understanding-the-population-structure-correction-regression"
"yearMonth" => "2022-07"
"year" => "2022"
"title" => "Understanding the Population Structure Correction Regression"
"description" => "MAI, T.T. et ALQUIER, P. (2022). Understanding the Population Structure Correction Regression. Dans: <i>4th International Conference on Statistics: Theory and Applications (ICSTA'22)</i>. Prague: Avestia Publishing. MAI, T.T. et ALQUIER, P. (2022). Understanding the Population Structure Correction Regression. Dans: "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MAI The Tien"
]
]
"ouvrage" => "4th International Conference on Statistics: Theory and Applications (ICSTA'22)"
"keywords" => array:5 [
0 => "GWAS"
1 => "population structure correction"
2 => "linear regression"
3 => "bias"
4 => "variance"
]
"updatedAt" => "2023-03-21 09:20:51"
"publicationUrl" => "https://doi.org/10.11159/icsta22.114"
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Although genome-wide association studies (GWAS) on complex traits have achieved great successes, the current leading GWAS approaches simply perform to test each genotype-phenotype association separately for each genetic variant. Curiously, the statistical property for using these approaches is not known when a joint model for the whole genetic variants is considered. Here we advance in GWAS in understanding the statistical properties of the “population structure correction” (PSC) approach, a standard univariate approach in GWAS. We further propose and analyse a correction to the PSC approach, termed as “corrected population correction” (CPC). Together with the theoretical results, numerical simulations show that CPC is always comparable or better than PSC, with a dramatic improvement in some special cases. - Although genome-wide association studies (GWAS) on complex traits have achieved great successes, the "
"en" => "Although genome-wide association studies (GWAS) on complex traits have achieved great successes, the current leading GWAS approaches simply perform to test each genotype-phenotype association separately for each genetic variant. Curiously, the statistical property for using these approaches is not known when a joint model for the whole genetic variants is considered. Here we advance in GWAS in understanding the statistical properties of the “population structure correction” (PSC) approach, a standard univariate approach in GWAS. We further propose and analyse a correction to the PSC approach, termed as “corrected population correction” (CPC). Together with the theoretical results, numerical simulations show that CPC is always comparable or better than PSC, with a dramatic improvement in some special cases. - Although genome-wide association studies (GWAS) on complex traits have achieved great successes, the "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
25 => Essec\Faculty\Model\Contribution {#2297
#_index: "academ_contributions"
#_id: "13870"
#_source: array:18 [
"id" => "13870"
"slug" => "13870-tight-risk-bound-for-high-dimensional-time-series-completion"
"yearMonth" => "2022-03"
"year" => "2022"
"title" => "Tight risk bound for high dimensional time series completion"
"description" => "ALQUIER, P., MARIE, N. et ROSIER, A. (2022). Tight risk bound for high dimensional time series completion. <i>The Electronic Journal of Statistics</i>, 16(1), pp. 3001-3035. ALQUIER, P., MARIE, N. et ROSIER, A. (2022). Tight risk bound for high dimensional time series compl "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MARIE Nicolas"
]
2 => array:1 [
"name" => "ROSIER Amélie"
]
]
"ouvrage" => ""
"keywords" => array:6 [
0 => "Matrix completion"
1 => "multivariate time series analysis"
2 => "matrix factorization"
3 => "high-dimensional time series"
4 => "concentration inequalities"
5 => "mixing"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/22-EJS2015"
"publicationInfo" => array:3 [
"pages" => "3001-3035"
"volume" => "16"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the application of these methods to dependent datas. In this paper, we propose a general model for multivariate, partially observed time series. We show that the least-square method with a rank penalty leads to reconstruction error of the same order as for independent datas. Moreover, when the time series has some additional properties such as periodicity or smoothness, the rate can actually be faster than in the independent case. Initially designed for independent datas, low-rank matrix completion was successfully applied in man "
"en" => "Initially designed for independent datas, low-rank matrix completion was successfully applied in many domains to the reconstruction of partially observed high-dimensional time series. However, there is a lack of theory to support the application of these methods to dependent datas. In this paper, we propose a general model for multivariate, partially observed time series. We show that the least-square method with a rank penalty leads to reconstruction error of the same order as for independent datas. Moreover, when the time series has some additional properties such as periodicity or smoothness, the rate can actually be faster than in the independent case. Initially designed for independent datas, low-rank matrix completion was successfully applied in man "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
26 => Essec\Faculty\Model\Contribution {#2298
#_index: "academ_contributions"
#_id: "13871"
#_source: array:18 [
"id" => "13871"
"slug" => "13871-finite-sample-properties-of-parametric-mmd-estimation-robustness-to-misspecification-and-dependence 13871-finite-sample-properties-of-parametric-mmd-estimation-robustness-to-misspecification-and-depen "
"yearMonth" => "2022-03"
"year" => "2022"
"title" => "Finite sample properties of parametric MMD estimation: Robustness to misspecification and dependence"
"description" => "CHERIEF-ABDELLATIF, B.E. et ALQUIER, P. (2022). Finite sample properties of parametric MMD estimation: Robustness to misspecification and dependence. <i>Bernoulli: A Journal of Mathematical Statistics and Probability</i>, 28(1), pp. 181-213. CHERIEF-ABDELLATIF, B.E. et ALQUIER, P. (2022). Finite sample properties of parametric MMD estimatio "
"authors" => array:2 [
0 => array:2 [
"name" => "CHERIEF-ABDELLATIF Badr-Eddine"
"bid" => "B00810114"
]
1 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-07-10 16:42:20"
"publicationUrl" => "https://doi.org/10.3150/21-BEJ1338"
"publicationInfo" => array:3 [
"pages" => "181-213"
"volume" => "28"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this distribution. This question is of major interest, in particular because the universality property leads to the robustness of the estimator. In this paper, we tackle the problem of universal estimation using a minimum distance estimator presented in (Briol et al. (2019)) based on the Maximum Mean Discrepancy. We show that the estimator is robust to both dependence and to the presence of outliers in the dataset. Finally, we provide a theoretical study of the stochastic gradient descent algorithm used to compute the estimator, and we support our findings with numerical simulations. Many works in statistics aim at designing a universal estimation procedure, that is, an estimator th "
"en" => "Many works in statistics aim at designing a universal estimation procedure, that is, an estimator that would converge to the best approximation of the (unknown) data generating distribution in a model, without any assumption on this distribution. This question is of major interest, in particular because the universality property leads to the robustness of the estimator. In this paper, we tackle the problem of universal estimation using a minimum distance estimator presented in (Briol et al. (2019)) based on the Maximum Mean Discrepancy. We show that the estimator is robust to both dependence and to the presence of outliers in the dataset. Finally, we provide a theoretical study of the stochastic gradient descent algorithm used to compute the estimator, and we support our findings with numerical simulations. Many works in statistics aim at designing a universal estimation procedure, that is, an estimator th "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
27 => Essec\Faculty\Model\Contribution {#2299
#_index: "academ_contributions"
#_id: "13879"
#_source: array:18 [
"id" => "13879"
"slug" => "13879-meta-strategy-for-learning-tuning-parameters-with-guarantees"
"yearMonth" => "2021-09"
"year" => "2021"
"title" => "Meta-Strategy for Learning Tuning Parameters with Guarantees"
"description" => "MEUNIER, D. et ALQUIER, P. (2021). Meta-Strategy for Learning Tuning Parameters with Guarantees. <i>Entropy</i>, 23(10). MEUNIER, D. et ALQUIER, P. (2021). Meta-Strategy for Learning Tuning Parameters with Guarantees. <i> "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MEUNIER Dimitri"
]
]
"ouvrage" => ""
"keywords" => array:7 [
0 => "meta-learning"
1 => "hyperparameters"
2 => "priors"
3 => "online learning"
4 => "Bayesian inference"
5 => "online optimization"
6 => "gradient descent"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.3390/e23101257"
"publicationInfo" => array:3 [
"pages" => null
"volume" => "23"
"number" => "10"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => "Suisse"
"en" => "Switzerland"
]
"abstract" => array:2 [
"fr" => "Online learning methods, similar to the online gradient algorithm (OGA) and exponentially weighted aggregation (EWA), often depend on tuning parameters that are difficult to set in practice. We consider an online meta-learning scenario, and we propose a meta-strategy to learn these parameters from past tasks. Our strategy is based on the minimization of a regret bound. It allows us to learn the initialization and the step size in OGA with guarantees. It also allows us to learn the prior or the learning rate in EWA. We provide a regret analysis of the strategy. It allows to identify settings where meta-learning indeed improves on learning each task in isolation. Online learning methods, similar to the online gradient algorithm (OGA) and exponentially weighted a "
"en" => "Online learning methods, similar to the online gradient algorithm (OGA) and exponentially weighted aggregation (EWA), often depend on tuning parameters that are difficult to set in practice. We consider an online meta-learning scenario, and we propose a meta-strategy to learn these parameters from past tasks. Our strategy is based on the minimization of a regret bound. It allows us to learn the initialization and the step size in OGA with guarantees. It also allows us to learn the prior or the learning rate in EWA. We provide a regret analysis of the strategy. It allows to identify settings where meta-learning indeed improves on learning each task in isolation. Online learning methods, similar to the online gradient algorithm (OGA) and exponentially weighted a "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
28 => Essec\Faculty\Model\Contribution {#2300
#_index: "academ_contributions"
#_id: "13880"
#_source: array:18 [
"id" => "13880"
"slug" => "13880-non-exponentially-weighted-aggregation-regret-bounds-for-unbounded-loss-functions"
"yearMonth" => "2021-07"
"year" => "2021"
"title" => "Non-exponentially Weighted Aggregation: Regret Bounds for Unbounded Loss Functions"
"description" => "ALQUIER, P. (2021). Non-exponentially Weighted Aggregation: Regret Bounds for Unbounded Loss Functions. Dans: <i>38th International Conference on Machine Learning (ICML'21)</i>. Proceedings of Machine Learning Research. ALQUIER, P. (2021). Non-exponentially Weighted Aggregation: Regret Bounds for Unbounded Loss Functio "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "38th International Conference on Machine Learning (ICML'21)"
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://proceedings.mlr.press/v139/alquier21a.html"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "Royaume-Uni"
"en" => "United Kingdom"
]
"abstract" => array:2 [
"fr" => "We tackle the problem of online optimization with a general, possibly unbounded, loss function. It is well known that when the loss is bounded, the exponentially weighted aggregation strategy (EWA) leads to a regret in √T after T steps. In this paper, we study a generalized aggregation strategy, where the weights no longer depend exponentially on the losses. Our strategy is based on Follow The Regularized Leader (FTRL): we minimize the expected losses plus a regularizer, that is here a ϕ-divergence. When the regularizer is the Kullback-Leibler divergence, we obtain EWA as a special case. Using alternative divergences enables unbounded losses, at the cost of a worst regret bound in some cases. We tackle the problem of online optimization with a general, possibly unbounded, loss function. It i "
"en" => "We tackle the problem of online optimization with a general, possibly unbounded, loss function. It is well known that when the loss is bounded, the exponentially weighted aggregation strategy (EWA) leads to a regret in √T after T steps. In this paper, we study a generalized aggregation strategy, where the weights no longer depend exponentially on the losses. Our strategy is based on Follow The Regularized Leader (FTRL): we minimize the expected losses plus a regularizer, that is here a ϕ-divergence. When the regularizer is the Kullback-Leibler divergence, we obtain EWA as a special case. Using alternative divergences enables unbounded losses, at the cost of a worst regret bound in some cases. We tackle the problem of online optimization with a general, possibly unbounded, loss function. It i "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
29 => Essec\Faculty\Model\Contribution {#2301
#_index: "academ_contributions"
#_id: "13881"
#_source: array:18 [
"id" => "13881"
"slug" => "13881-a-theoretical-analysis-of-catastrophic-forgetting-through-the-ntk-overlap-matrix"
"yearMonth" => "2021-04"
"year" => "2021"
"title" => "A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix"
"description" => "DOAN, T., ABBANA BENNANI, M., MAZOURE, B., RABUSSEAU, G. et ALQUIER, P. (2021). A Theoretical Analysis of Catastrophic Forgetting through the NTK Overlap Matrix. Dans: <i>24th International Conference on Artificial Intelligence and Statistics (AIStat'21)</i>. Proceedings of Machine Learning Research. DOAN, T., ABBANA BENNANI, M., MAZOURE, B., RABUSSEAU, G. et ALQUIER, P. (2021). A Theoretical Analys "
"authors" => array:5 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "DOAN Tang"
]
2 => array:1 [
"name" => "ABBANA BENNANI Mehdi"
]
3 => array:1 [
"name" => "MAZOURE Bogdan"
]
4 => array:1 [
"name" => "RABUSSEAU Guillaume"
]
]
"ouvrage" => "24th International Conference on Artificial Intelligence and Statistics (AIStat'21)"
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://proceedings.mlr.press/v130/doan21a.html"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "Royaume-Uni"
"en" => "United Kingdom"
]
"abstract" => array:2 [
"fr" => "Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data during its entire lifetime. Although major advances have been made in the field, one recurring problem which remains unsolved is that of Catastrophic Forgetting (CF). While the issue has been extensively studied empirically, little attention has been paid from a theoretical angle. In this paper, we show that the impact of CF increases as two tasks increasingly align. We introduce a measure of task similarity called the NTK overlap matrix which is at the core of CF. We analyze common projected gradient algorithms and demonstrate how they mitigate forgetting. Then, we propose a variant of Orthogonal Gradient Descent (OGD) which leverages structure of the data through Principal Component Analysis (PCA). Experiments support our theoretical findings and show how our method can help reduce CF on classical CL datasets. Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data "
"en" => "Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data during its entire lifetime. Although major advances have been made in the field, one recurring problem which remains unsolved is that of Catastrophic Forgetting (CF). While the issue has been extensively studied empirically, little attention has been paid from a theoretical angle. In this paper, we show that the impact of CF increases as two tasks increasingly align. We introduce a measure of task similarity called the NTK overlap matrix which is at the core of CF. We analyze common projected gradient algorithms and demonstrate how they mitigate forgetting. Then, we propose a variant of Orthogonal Gradient Descent (OGD) which leverages structure of the data through Principal Component Analysis (PCA). Experiments support our theoretical findings and show how our method can help reduce CF on classical CL datasets. Continual learning (CL) is a setting in which an agent has to learn from an incoming stream of data "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
30 => Essec\Faculty\Model\Contribution {#2302
#_index: "academ_contributions"
#_id: "13882"
#_source: array:18 [
"id" => "13882"
"slug" => "13882-simultaneous-dimension-reduction-and-clustering-via-the-nmf-em-algorithm"
"yearMonth" => "2021-03"
"year" => "2021"
"title" => "Simultaneous dimension reduction and clustering via the NMF-EM algorithm"
"description" => "CAREL, L. et ALQUIER, P. (2021). Simultaneous dimension reduction and clustering via the NMF-EM algorithm. <i>Advances in Data Analysis and Classification</i>, 15(1), pp. 231-260. CAREL, L. et ALQUIER, P. (2021). Simultaneous dimension reduction and clustering via the NMF-EM algo "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "CAREL Léna"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 09:28:55"
"publicationUrl" => "https://link.springer.com/article/10.1007/s11634-020-00398-4"
"publicationInfo" => array:3 [
"pages" => "231-260"
"volume" => "15"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Mixture models are among the most popular tools for clustering. However, when the dimension and the number of clusters is large, the estimation of the clusters become challenging, as well as their interpretation. Restriction on the parameters can be used to reduce the dimension. An example is given by mixture of factor analyzers for Gaussian mixtures. The extension of MFA to non-Gaussian mixtures is not straightforward. We propose a new constraint for parameters in non-Gaussian mixture model: the K components parameters are combinations of elements from a small dictionary, say H elements, with H≪K. Including a nonnegative matrix factorization (NMF) in the EM algorithm allows us to simultaneously estimate the dictionary and the parameters of the mixture. We propose the acronym NMF-EM for this algorithm, implemented in the R package nmfem. This original approach is motivated by passengers clustering from ticketing data: we apply NMF-EM to data from two Transdev public transport networks. In this case, the words are easily interpreted as typical slots in a timetable. Mixture models are among the most popular tools for clustering. However, when the dimension and the "
"en" => "Mixture models are among the most popular tools for clustering. However, when the dimension and the number of clusters is large, the estimation of the clusters become challenging, as well as their interpretation. Restriction on the parameters can be used to reduce the dimension. An example is given by mixture of factor analyzers for Gaussian mixtures. The extension of MFA to non-Gaussian mixtures is not straightforward. We propose a new constraint for parameters in non-Gaussian mixture model: the K components parameters are combinations of elements from a small dictionary, say H elements, with H≪K. Including a nonnegative matrix factorization (NMF) in the EM algorithm allows us to simultaneously estimate the dictionary and the parameters of the mixture. We propose the acronym NMF-EM for this algorithm, implemented in the R package nmfem. This original approach is motivated by passengers clustering from ticketing data: we apply NMF-EM to data from two Transdev public transport networks. In this case, the words are easily interpreted as typical slots in a timetable. Mixture models are among the most popular tools for clustering. However, when the dimension and the "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
31 => Essec\Faculty\Model\Contribution {#2303
#_index: "academ_contributions"
#_id: "13884"
#_source: array:18 [
"id" => "13884"
"slug" => "13884-approximate-bayesian-inference"
"yearMonth" => "2022-05"
"year" => "2022"
"title" => "Approximate Bayesian Inference"
"description" => "ALQUIER, P. [Ed] (2022). <i>Approximate Bayesian Inference</i>. MDPI."
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:11 [
0 => "Bayesian statistics"
1 => "machine learning"
2 => "variational approximations"
3 => "PAC-Bayes"
4 => "expectation-propagation"
5 => "Markov chain Monte Carlo"
6 => "Langevin Monte Carlo"
7 => "sequential Monte Carlo"
8 => "Laplace approximations"
9 => "approximate Bayesian computation"
10 => "Gibbs posterior"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://www.mdpi.com/books/book/5544"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Direction d'ouvrage"
"en" => "Book editor"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => """
This book is a reprint of the Special Issue Approximate Bayesian Inference that was published in the open access journal Entropy (ISSN 1099-4300) (available at: https://www.mdpi.com/journal/entropy/special_issues/approx_Bayes_inference).\n This book is a reprint of the Special Issue Approximate Bayesian Inference that was published in the
The objective of this Special Issue is to provide the latest advances in approximate Monte Carlo methods and in approximations of the posterior: design of efficient algorithms, study of the statistical properties of these algorithms, and challenging applications. The objective of this Special Issue is to provide the latest advances in approximate Monte Carlo met
"""
"en" => """
This book is a reprint of the Special Issue Approximate Bayesian Inference that was published in the open access journal Entropy (ISSN 1099-4300) (available at: https://www.mdpi.com/journal/entropy/special_issues/approx_Bayes_inference).\n This book is a reprint of the Special Issue Approximate Bayesian Inference that was published in the
The objective of this Special Issue is to provide the latest advances in approximate Monte Carlo methods and in approximations of the posterior: design of efficient algorithms, study of the statistical properties of these algorithms, and challenging applications. The objective of this Special Issue is to provide the latest advances in approximate Monte Carlo met
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
32 => Essec\Faculty\Model\Contribution {#2304
#_index: "academ_contributions"
#_id: "13885"
#_source: array:18 [
"id" => "13885"
"slug" => "13885-approximate-bayesian-inference"
"yearMonth" => "2020-11"
"year" => "2020"
"title" => "Approximate Bayesian Inference"
"description" => "ALQUIER, P. (2020). Approximate Bayesian Inference. <i>Entropy</i>, 22(11), pp. 1272."
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:11 [
0 => "Bayesian statistics"
1 => "machine learning"
2 => "variational approximations"
3 => "PAC-Bayes"
4 => "expectation-propagation"
5 => "Markov chain Monte Carlo"
6 => "Langevin Monte Carlo"
7 => "sequential Monte Carlo"
8 => "Laplace approximations"
9 => "approximate Bayesian computation"
10 => "Gibbs posterior"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://www.mdpi.com/1099-4300/22/11/1272"
"publicationInfo" => array:3 [
"pages" => "1272"
"volume" => "22"
"number" => "11"
]
"type" => array:2 [
"fr" => "Préfaces / Introductions de revue"
"en" => "Prefaces of a journal"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => "Suisse"
"en" => "Switzerland"
]
"abstract" => array:2 [
"fr" => "This is the Editorial article summarizing the scope of the Special Issue: Approximate Bayesian Inference. This is the Editorial article summarizing the scope of the Special Issue: Approximate Bayesian Infer "
"en" => "This is the Editorial article summarizing the scope of the Special Issue: Approximate Bayesian Inference. This is the Editorial article summarizing the scope of the Special Issue: Approximate Bayesian Infer "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
33 => Essec\Faculty\Model\Contribution {#2305
#_index: "academ_contributions"
#_id: "13887"
#_source: array:18 [
"id" => "13887"
"slug" => "13887-high-dimensional-var-with-low-rank-transition"
"yearMonth" => "2020-07"
"year" => "2020"
"title" => "High-dimensional VAR with low-rank transition"
"description" => "ALQUIER, P., BERTIN, K., DOUKHAN, P. et GARNIER, R. (2020). High-dimensional VAR with low-rank transition. <i>Statistics and Computing</i>, 30(4), pp. 1139-1153. ALQUIER, P., BERTIN, K., DOUKHAN, P. et GARNIER, R. (2020). High-dimensional VAR with low-rank trans "
"authors" => array:4 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "BERTIN Karine"
]
2 => array:1 [
"name" => "DOUKHAN Paul"
]
3 => array:1 [
"name" => "GARNIER Rémy"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 09:36:35"
"publicationUrl" => "https://link.springer.com/article/10.1007/s11222-020-09929-7"
"publicationInfo" => array:3 [
"pages" => "1139-1153"
"volume" => "30"
"number" => "4"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden factors. While our model has formal similarities with factor models, its structure is more a way to reduce the dimension in order to improve the predictions, rather than a way to define interpretable factors. We provide an estimator for the transition matrix in a very general setting and study its performances in terms of prediction and adaptation to the unknown rank. Our method obtains good result on simulated data, in particular when the rank of the underlying process is small. On macroeconomic data from Giannone et al. (Rev Econ Stat 97(2):436–451, 2015), our method is competitive with state-of-the-art methods in small dimension and even improves on them in high dimension. We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This "
"en" => "We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden factors. While our model has formal similarities with factor models, its structure is more a way to reduce the dimension in order to improve the predictions, rather than a way to define interpretable factors. We provide an estimator for the transition matrix in a very general setting and study its performances in terms of prediction and adaptation to the unknown rank. Our method obtains good result on simulated data, in particular when the rank of the underlying process is small. On macroeconomic data from Giannone et al. (Rev Econ Stat 97(2):436–451, 2015), our method is competitive with state-of-the-art methods in small dimension and even improves on them in high dimension. We propose a vector auto-regressive model with a low-rank constraint on the transition matrix. This "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
34 => Essec\Faculty\Model\Contribution {#2306
#_index: "academ_contributions"
#_id: "13889"
#_source: array:18 [
"id" => "13889"
"slug" => "13889-mmd-bayes-robust-bayesian-estimation-via-maximum-mean-discrepancy"
"yearMonth" => "2020-01"
"year" => "2020"
"title" => "MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy"
"description" => "CHERIEF-ABDELLATIF, B.E. et ALQUIER, P. (2020). MMD-Bayes: Robust Bayesian Estimation via Maximum Mean Discrepancy. Dans: <i>2nd Symposium on Advances in Approximate Bayesian Inference (AABI'19)</i>. Proceedings of Machine Learning Research. CHERIEF-ABDELLATIF, B.E. et ALQUIER, P. (2020). MMD-Bayes: Robust Bayesian Estimation via Maximum Me "
"authors" => array:2 [
0 => array:2 [
"name" => "CHERIEF-ABDELLATIF Badr-Eddine"
"bid" => "B00810114"
]
1 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "2nd Symposium on Advances in Approximate Bayesian Inference (AABI'19)"
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://proceedings.mlr.press/v118/cherief-abdellatif20a.html"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "Royaume-Uni"
"en" => "United Kingdom"
]
"abstract" => array:2 [
"fr" => "In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties. In this paper, we build a pseudo-likelihood based on the Maximum Mean Discrepancy, dened via an embedding of probability distributions into a reproducing kernel Hilbert space. We show that this MMD-Bayes posterior is consistent and robust to model misspecication. As the posterior obtained in this way might be intractable, we also prove that reasonable variational approximations of this posterior enjoy the same properties. We provide details on a stochastic gradient algorithm to compute these variational approximations. Numerical simulations indeed suggest that our estimator is more robust to misspecication than the ones based on the likelihood. In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsi "
"en" => "In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties. In this paper, we build a pseudo-likelihood based on the Maximum Mean Discrepancy, dened via an embedding of probability distributions into a reproducing kernel Hilbert space. We show that this MMD-Bayes posterior is consistent and robust to model misspecication. As the posterior obtained in this way might be intractable, we also prove that reasonable variational approximations of this posterior enjoy the same properties. We provide details on a stochastic gradient algorithm to compute these variational approximations. Numerical simulations indeed suggest that our estimator is more robust to misspecication than the ones based on the likelihood. In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsi "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
35 => Essec\Faculty\Model\Contribution {#2307
#_index: "academ_contributions"
#_id: "13890"
#_source: array:18 [
"id" => "13890"
"slug" => "13890-matrix-factorization-for-multivariate-time-series-analysis"
"yearMonth" => "2019-11"
"year" => "2019"
"title" => "Matrix factorization for multivariate time series analysis"
"description" => "ALQUIER, P. et MARIE, N. (2019). Matrix factorization for multivariate time series analysis. <i>The Electronic Journal of Statistics</i>, 13(2), pp. 4346-4366. ALQUIER, P. et MARIE, N. (2019). Matrix factorization for multivariate time series analysis. <i>The "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MARIE Nicolas"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "Multivariate Time Series Analysis"
1 => "matrix Factorization"
2 => "random Matrices"
3 => "non-parametric Regression"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-13/issue-2/Matrix-factorization-for-multivariate-time-series-analysis/10.1214/19-EJS1630.full https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-13/issue-2/Matrix-factori "
"publicationInfo" => array:3 [
"pages" => "4346-4366"
"volume" => "13"
"number" => "2"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical performances of matrix factorization for time series. In this paper, we extend the results known for matrix estimation in the i.i.d setting to time series. Moreover, we prove that when the series exhibit some additional structure like periodicity or smoothness, it is possible to improve on the classical rates of convergence. Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series "
"en" => "Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series analysis, leading to the decomposition of the series in a small set of latent factors. However, little is known on the statistical performances of matrix factorization for time series. In this paper, we extend the results known for matrix estimation in the i.i.d setting to time series. Moreover, we prove that when the series exhibit some additional structure like periodicity or smoothness, it is possible to improve on the classical rates of convergence. Matrix factorization is a powerful data analysis tool. It has been used in multivariate time series "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
36 => Essec\Faculty\Model\Contribution {#2308
#_index: "academ_contributions"
#_id: "13891"
#_source: array:18 [
"id" => "13891"
"slug" => "13891-a-generalization-bound-for-online-variational-inference"
"yearMonth" => "2019-11"
"year" => "2019"
"title" => "A Generalization Bound for Online Variational Inference"
"description" => "CHERIEF-ABDELLATIF, B.E., ALQUIER, P. et KHAN, M.E. (2019). A Generalization Bound for Online Variational Inference. Dans: <i>11th Asian Conference on Machine Learning (ACML'19)</i>. Proceedings of Machine Learning Research. CHERIEF-ABDELLATIF, B.E., ALQUIER, P. et KHAN, M.E. (2019). A Generalization Bound for Online Variat "
"authors" => array:3 [
0 => array:2 [
"name" => "CHERIEF-ABDELLATIF Badr-Eddine"
"bid" => "B00810114"
]
1 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
2 => array:1 [
"name" => "KHAN Mohammad Emtiyaz"
]
]
"ouvrage" => "11th Asian Conference on Machine Learning (ACML'19)"
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://proceedings.mlr.press/v101/cherief-abdellatif19a.html"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "Royaume-Uni"
"en" => "United Kingdom"
]
"abstract" => array:2 [
"fr" => "Bayesian inference provides an attractive online-learning framework to analyze sequential data, and offers generalization guarantees which hold even with model mismatch and adversaries. Unfortunately, exact Bayesian inference is rarely feasible in practice and approximation methods are usually employed, but do such methods preserve the generalization properties of Bayesian inference? In this paper, we show that this is indeed the case for some variational inference (VI) algorithms. We consider a few existing online, tempered VI algorithms, as well as a new algorithm, and derive their generalization bounds. Our theoretical result relies on the convexity of the variational objective, but we argue that the result should hold more generally and present empirical evidence in support of this. Our work in this paper presents theoretical justifications in favor of online algorithms relying on approximate Bayesian methods. Bayesian inference provides an attractive online-learning framework to analyze sequential data, and "
"en" => "Bayesian inference provides an attractive online-learning framework to analyze sequential data, and offers generalization guarantees which hold even with model mismatch and adversaries. Unfortunately, exact Bayesian inference is rarely feasible in practice and approximation methods are usually employed, but do such methods preserve the generalization properties of Bayesian inference? In this paper, we show that this is indeed the case for some variational inference (VI) algorithms. We consider a few existing online, tempered VI algorithms, as well as a new algorithm, and derive their generalization bounds. Our theoretical result relies on the convexity of the variational objective, but we argue that the result should hold more generally and present empirical evidence in support of this. Our work in this paper presents theoretical justifications in favor of online algorithms relying on approximate Bayesian methods. Bayesian inference provides an attractive online-learning framework to analyze sequential data, and "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
37 => Essec\Faculty\Model\Contribution {#2309
#_index: "academ_contributions"
#_id: "13892"
#_source: array:18 [
"id" => "13892"
"slug" => "13892-exponential-inequalities-for-nonstationary-markov-chains"
"yearMonth" => "2019-06"
"year" => "2019"
"title" => "Exponential inequalities for nonstationary Markov chains"
"description" => "ALQUIER, P., DOUKHAN, P. et FAN, X. (2019). Exponential inequalities for nonstationary Markov chains. <i>Dependence Modeling</i>, 7(1), pp. 150-168. ALQUIER, P., DOUKHAN, P. et FAN, X. (2019). Exponential inequalities for nonstationary Markov chains "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "DOUKHAN Paul"
]
2 => array:1 [
"name" => "FAN Xiequan"
]
]
"ouvrage" => ""
"keywords" => array:7 [
0 => "Nonstationary Markov chains"
1 => "Martingales"
2 => "Exponential inequalities"
3 => "Time series forecasting"
4 => "Sta-tistical learning theory"
5 => "Oracle inequalities"
6 => "Model selection"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://www.degruyter.com/document/doi/10.1515/demo-2019-0007/html?lang=en"
"publicationInfo" => array:3 [
"pages" => "150-168"
"volume" => "7"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on inequalities and learning theory for time series, in the past 15 years. How-ever, for the non-independent case, almost all the results concern stationary time series. This excludes many important applications: for example any series with a periodic behaviour is nonstationary. In this paper, we extend the basic tools of [19] to nonstationary Markov chains. As an application, we provide a Bernstein-type inequality, and we deduce risk bounds for the prediction of periodic autoregressive processes with an unknown period Exponential inequalities are main tools in machine learning theory. To prove exponential inequalitie "
"en" => "Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on inequalities and learning theory for time series, in the past 15 years. How-ever, for the non-independent case, almost all the results concern stationary time series. This excludes many important applications: for example any series with a periodic behaviour is nonstationary. In this paper, we extend the basic tools of [19] to nonstationary Markov chains. As an application, we provide a Bernstein-type inequality, and we deduce risk bounds for the prediction of periodic autoregressive processes with an unknown period Exponential inequalities are main tools in machine learning theory. To prove exponential inequalitie "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
38 => Essec\Faculty\Model\Contribution {#2310
#_index: "academ_contributions"
#_id: "13893"
#_source: array:18 [
"id" => "13893"
"slug" => "13893-informed-sub-sampling-mcmc-approximate-bayesian-inference-for-large-datasets"
"yearMonth" => "2019-05"
"year" => "2019"
"title" => "Informed sub-sampling MCMC: approximate Bayesian inference for large datasets"
"description" => "MAIRE, F., FRIEL, N. et ALQUIER, P. (2019). Informed sub-sampling MCMC: approximate Bayesian inference for large datasets. <i>Statistics and Computing</i>, 29(3), pp. 449-482. MAIRE, F., FRIEL, N. et ALQUIER, P. (2019). Informed sub-sampling MCMC: approximate Bayesian inferen "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MAIRE Florian"
]
2 => array:1 [
"name" => "FRIEL Nial"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 09:45:27"
"publicationUrl" => "https://link.springer.com/article/10.1007/s11222-018-9817-3"
"publicationInfo" => array:3 [
"pages" => "449-482"
"volume" => "29"
"number" => "3"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an unknown fraction of fixed size of the available data that is randomly refreshed throughout the algorithm. Inspired by the Approximate Bayesian Computation literature, the subsampling process is guided by the fidelity to the observed data, as measured by summary statistics. The resulting algorithm, Informed Sub-Sampling MCMC, is a generic and flexible approach which, contrary to existing scalable methodologies, preserves the simplicity of the Metropolis–Hastings algorithm. Even though exactness is lost, i.e. the chain distribution approximates the posterior, we study and quantify theoretically this bias and show on a diverse set of examples that it yields excellent performances when the computational budget is limited. If available and cheap to compute, we show that setting the summary statistics as the maximum likelihood estimator is supported by theoretical arguments. This paper introduces a framework for speeding up Bayesian inference conducted in presence of large "
"en" => "This paper introduces a framework for speeding up Bayesian inference conducted in presence of large datasets. We design a Markov chain whose transition kernel uses an unknown fraction of fixed size of the available data that is randomly refreshed throughout the algorithm. Inspired by the Approximate Bayesian Computation literature, the subsampling process is guided by the fidelity to the observed data, as measured by summary statistics. The resulting algorithm, Informed Sub-Sampling MCMC, is a generic and flexible approach which, contrary to existing scalable methodologies, preserves the simplicity of the Metropolis–Hastings algorithm. Even though exactness is lost, i.e. the chain distribution approximates the posterior, we study and quantify theoretically this bias and show on a diverse set of examples that it yields excellent performances when the computational budget is limited. If available and cheap to compute, we show that setting the summary statistics as the maximum likelihood estimator is supported by theoretical arguments. This paper introduces a framework for speeding up Bayesian inference conducted in presence of large "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
39 => Essec\Faculty\Model\Contribution {#2311
#_index: "academ_contributions"
#_id: "13894"
#_source: array:18 [
"id" => "13894"
"slug" => "13894-1-bit-matrix-completion-pac-bayesian-analysis-of-a-variational-approximation"
"yearMonth" => "2018-03"
"year" => "2018"
"title" => "1-Bit matrix completion: PAC-Bayesian analysis of a variational approximation"
"description" => "COTTET, V. et ALQUIER, P. (2018). 1-Bit matrix completion: PAC-Bayesian analysis of a variational approximation. <i>Machine Learning</i>, 107(3), pp. 579-603. COTTET, V. et ALQUIER, P. (2018). 1-Bit matrix completion: PAC-Bayesian analysis of a variational ap "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "COTTET Vincent"
]
]
"ouvrage" => ""
"keywords" => array:1 [
0 => "Bayesian analysis"
]
"updatedAt" => "2023-07-10 17:29:05"
"publicationUrl" => "https://link.springer.com/article/10.1007/s10994-017-5667-z"
"publicationInfo" => array:3 [
"pages" => "579-603"
"volume" => "107"
"number" => "3"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
"abstract" => array:2 [
"fr" => "We focus on the completion of a (possibly) low-rank matrix with binary entries, the so-called 1-bit matrix completion problem. Our approach relies on tools from machine learning theory: empirical risk minimization and its convex relaxations. We propose an algorithm to compute a variational approximation of the pseudo-posterior. Thanks to the convex relaxation, the corresponding minimization problem is bi-convex, and thus the method works well in practice. We study the performance of this variational approximation through PAC-Bayesian learning bounds. Contrary to previous works that focused on upper bounds on the estimation error of M with various matrix norms, we are able to derive from this analysis a PAC bound on the prediction error of our algorithm. We focus essentially on convex relaxation through the hinge loss, for which we present a complete analysis, a complete simulation study and a test on the MovieLens data set. We also discuss a variational approximation to deal with the logistic loss. We focus on the completion of a (possibly) low-rank matrix with binary entries, the so-called 1-bit "
"en" => "We focus on the completion of a (possibly) low-rank matrix with binary entries, the so-called 1-bit matrix completion problem. Our approach relies on tools from machine learning theory: empirical risk minimization and its convex relaxations. We propose an algorithm to compute a variational approximation of the pseudo-posterior. Thanks to the convex relaxation, the corresponding minimization problem is bi-convex, and thus the method works well in practice. We study the performance of this variational approximation through PAC-Bayesian learning bounds. Contrary to previous works that focused on upper bounds on the estimation error of M with various matrix norms, we are able to derive from this analysis a PAC bound on the prediction error of our algorithm. We focus essentially on convex relaxation through the hinge loss, for which we present a complete analysis, a complete simulation study and a test on the MovieLens data set. We also discuss a variational approximation to deal with the logistic loss. We focus on the completion of a (possibly) low-rank matrix with binary entries, the so-called 1-bit "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
40 => Essec\Faculty\Model\Contribution {#2312
#_index: "academ_contributions"
#_id: "13895"
#_source: array:18 [
"id" => "13895"
"slug" => "13895-pseudo-bayesian-quantum-tomography-with-rank-adaptation"
"yearMonth" => "2017-05"
"year" => "2017"
"title" => "Pseudo-Bayesian quantum tomography with rank-adaptation"
"description" => "MAI, T.T. et ALQUIER, P. (2017). Pseudo-Bayesian quantum tomography with rank-adaptation. <i>Journal of Statistical Planning and Inference</i>, 184, pp. 62-76. MAI, T.T. et ALQUIER, P. (2017). Pseudo-Bayesian quantum tomography with rank-adaptation. <i>Journal "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MAI The Tien"
]
]
"ouvrage" => ""
"keywords" => array:5 [
0 => "Quantum statistics"
1 => "Bayesian statistics"
2 => "PAC-Bayesian bounds"
3 => "Oracle inequalities"
4 => "MCMC"
]
"updatedAt" => "2023-03-22 09:51:22"
"publicationUrl" => "https://doi.org/10.1016/j.jspi.2016.11.003"
"publicationInfo" => array:3 [
"pages" => "62-76"
"volume" => "184"
"number" => ""
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choices in estimating quantum states (Blume-Kohout, 2010). Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of 1-qubit state recovery. However, the problem of choosing prior distribution in the general case of n qubits is not straightforward. More importantly, the statistical performance of Bayesian type estimators has not been studied from a theoretical perspective yet. In this paper, we propose a novel prior for quantum states (density matrices), and we define pseudo-Bayesian estimators of the density matrix. Then, using PAC-Bayesian theorems (Catoni, 2007), we derive rates of convergence for the posterior mean. The numerical performance of these estimators is tested on simulated and real datasets. Quantum state tomography, an important task in quantum information processing, aims at reconstructin "
"en" => "Quantum state tomography, an important task in quantum information processing, aims at reconstructing a state from prepared measurement data. Bayesian methods are recognized to be one of the good and reliable choices in estimating quantum states (Blume-Kohout, 2010). Several numerical works showed that Bayesian estimations are comparable to, and even better than other methods in the problem of 1-qubit state recovery. However, the problem of choosing prior distribution in the general case of n qubits is not straightforward. More importantly, the statistical performance of Bayesian type estimators has not been studied from a theoretical perspective yet. In this paper, we propose a novel prior for quantum states (density matrices), and we define pseudo-Bayesian estimators of the density matrix. Then, using PAC-Bayesian theorems (Catoni, 2007), we derive rates of convergence for the posterior mean. The numerical performance of these estimators is tested on simulated and real datasets. Quantum state tomography, an important task in quantum information processing, aims at reconstructin "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
41 => Essec\Faculty\Model\Contribution {#2313
#_index: "academ_contributions"
#_id: "13896"
#_source: array:18 [
"id" => "13896"
"slug" => "13896-regret-bounds-for-lifelong-learning"
"yearMonth" => "2017-04"
"year" => "2017"
"title" => "Regret Bounds for Lifelong Learning"
"description" => "ALQUIER, P., MAI, T.T. et PONTIL, M. (2017). Regret Bounds for Lifelong Learning. Dans: <i>20th International Conference on Artificial Intelligence and Statistics (AIStat'17)</i>. Proceedings of Machine Learning Research. ALQUIER, P., MAI, T.T. et PONTIL, M. (2017). Regret Bounds for Lifelong Learning. Dans: <i>20th Inte "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MAI The Tien"
]
2 => array:1 [
"name" => "PONTIL Massimiliano"
]
]
"ouvrage" => "20th International Conference on Artificial Intelligence and Statistics (AIStat'17)"
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://proceedings.mlr.press/v54/alquier17a.html"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "Royaume-Uni"
"en" => "United Kingdom"
]
"abstract" => array:2 [
"fr" => "We consider the problem of transfer learning in an online setting. Different tasks are presented sequentially and processed by a within-task algorithm. We propose a lifelong learning strategy which refines the underlying data representation used by the within-task algorithm, thereby transferring information from one task to the next. We show that when the within-task algorithm comes with some regret bound, our strategy inherits this good property. Our bounds are in expectation for a general loss function, and uniform for a convex loss. We discuss applications to dictionary learning and finite set of predictors. We consider the problem of transfer learning in an online setting. Different tasks are presented seq "
"en" => "We consider the problem of transfer learning in an online setting. Different tasks are presented sequentially and processed by a within-task algorithm. We propose a lifelong learning strategy which refines the underlying data representation used by the within-task algorithm, thereby transferring information from one task to the next. We show that when the within-task algorithm comes with some regret bound, our strategy inherits this good property. Our bounds are in expectation for a general loss function, and uniform for a convex loss. We discuss applications to dictionary learning and finite set of predictors. We consider the problem of transfer learning in an online setting. Different tasks are presented seq "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
42 => Essec\Faculty\Model\Contribution {#2314
#_index: "academ_contributions"
#_id: "13897"
#_source: array:18 [
"id" => "13897"
"slug" => "13897-non-negative-matrix-factorization-as-a-pre-processing-tool-for-travelers-temporal-profiles-clustering 13897-non-negative-matrix-factorization-as-a-pre-processing-tool-for-travelers-temporal-profiles-clu "
"yearMonth" => "2017-04"
"year" => "2017"
"title" => "Non-negative Matrix Factorization as a Pre-processing tool for Travelers Temporal Profiles Clustering Non-negative Matrix Factorization as a Pre-processing tool for Travelers Temporal Profiles Clusterin "
"description" => "CAREL, L. et ALQUIER, P. (2017). Non-negative Matrix Factorization as a Pre-processing tool for Travelers Temporal Profiles Clustering. Dans: <i>25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN'17)</i>. i6doc.com. CAREL, L. et ALQUIER, P. (2017). Non-negative Matrix Factorization as a Pre-processing tool for Trav "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "CAREL Léna"
]
]
"ouvrage" => "25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learning (ESANN'17) 25th European Symposium on Artificial Neural Networks, Computational Intelligence and Machine Learni "
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "Belgique"
"en" => "Belgium"
]
"abstract" => array:2 [
"fr" => null
"en" => null
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
43 => Essec\Faculty\Model\Contribution {#2315
#_index: "academ_contributions"
#_id: "13898"
#_source: array:18 [
"id" => "13898"
"slug" => "13898-an-oracle-inequality-for-quasi-bayesian-nonnegative-matrix-factorization"
"yearMonth" => "2017-01"
"year" => "2017"
"title" => "An oracle inequality for quasi-Bayesian nonnegative matrix factorization"
"description" => "ALQUIER, P. et GUEDJ, B. (2017). An oracle inequality for quasi-Bayesian nonnegative matrix factorization. <i>Mathematical Methods of Statistics</i>, 26(1), pp. 55-67. ALQUIER, P. et GUEDJ, B. (2017). An oracle inequality for quasi-Bayesian nonnegative matrix factoriz "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "GUEDJ B."
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 09:53:05"
"publicationUrl" => "https://link.springer.com/article/10.3103/S1066530717010045"
"publicationInfo" => array:3 [
"pages" => "55-67"
"volume" => "26"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods of nonnegative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergence. The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation met "
"en" => "The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation methods of nonnegative matrix factorization. We derive an oracle inequality for an aggregated estimator. This result holds for a very general class of prior distributions and shows how the prior affects the rate of convergence. The aim of this paper is to provide some theoretical understanding of quasi-Bayesian aggregation met "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
44 => Essec\Faculty\Model\Contribution {#2316
#_index: "academ_contributions"
#_id: "13899"
#_source: array:18 [
"id" => "13899"
"slug" => "13899-on-the-properties-of-variational-approximations-of-gibbs-posteriors"
"yearMonth" => "2016-12"
"year" => "2016"
"title" => "On the Properties of Variational Approximations of Gibbs Posteriors"
"description" => "ALQUIER, P., RIDGWAY, J. et CHOPIN, N. (2016). On the Properties of Variational Approximations of Gibbs Posteriors. <i>Journal of Machine Learning Research</i>, 17(239), pp. 1-41. ALQUIER, P., RIDGWAY, J. et CHOPIN, N. (2016). On the Properties of Variational Approximations of Gi "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "RIDGWAY James"
]
2 => array:1 [
"name" => "CHOPIN Nicolas"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://www.jmlr.org/papers/v17/15-290.html"
"publicationInfo" => array:3 [
"pages" => "1-41"
"volume" => "17"
"number" => "239"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
"abstract" => array:2 [
"fr" => "The PAC-Bayesian approach is a powerful set of techniques to derive non-asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately often intractable. One may sample from it using Markov chain Monte Carlo, but this is usually too slow for big datasets. We consider instead variational approximations of the Gibbs posterior, which are fast to compute. We undertake a general study of the properties of such approximations. Our main finding is that such a variational approximation has often the same rate of convergence as the original PAC-Bayesian procedure it approximates. In addition, we show that, when the risk function is convex, a variational approximation can be obtained in polynomial time using a convex solver. We give finite sample oracle inequalities for the corresponding estimator. We specialize our results to several learning tasks (classification, ranking, matrix completion), discuss how to implement a variational approximation in each case, and illustrate the good properties of said approximation on real datasets. The PAC-Bayesian approach is a powerful set of techniques to derive non-asymptotic risk bounds for r "
"en" => "The PAC-Bayesian approach is a powerful set of techniques to derive non-asymptotic risk bounds for random estimators. The corresponding optimal distribution of estimators, usually called the Gibbs posterior, is unfortunately often intractable. One may sample from it using Markov chain Monte Carlo, but this is usually too slow for big datasets. We consider instead variational approximations of the Gibbs posterior, which are fast to compute. We undertake a general study of the properties of such approximations. Our main finding is that such a variational approximation has often the same rate of convergence as the original PAC-Bayesian procedure it approximates. In addition, we show that, when the risk function is convex, a variational approximation can be obtained in polynomial time using a convex solver. We give finite sample oracle inequalities for the corresponding estimator. We specialize our results to several learning tasks (classification, ranking, matrix completion), discuss how to implement a variational approximation in each case, and illustrate the good properties of said approximation on real datasets. The PAC-Bayesian approach is a powerful set of techniques to derive non-asymptotic risk bounds for r "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
45 => Essec\Faculty\Model\Contribution {#2317
#_index: "academ_contributions"
#_id: "13900"
#_source: array:18 [
"id" => "13900"
"slug" => "13900-noisy-monte-carlo-convergence-of-markov-chains-with-approximate-transition-kernels"
"yearMonth" => "2016-01"
"year" => "2016"
"title" => "Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels"
"description" => "ALQUIER, P., FRIEL, N., EVERITT, R. et BOLAND, A. (2016). Noisy Monte Carlo: convergence of Markov chains with approximate transition kernels. <i>Statistics and Computing</i>, 26(1-2), pp. 29-47. ALQUIER, P., FRIEL, N., EVERITT, R. et BOLAND, A. (2016). Noisy Monte Carlo: convergence of Markov c "
"authors" => array:4 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "FRIEL N."
]
2 => array:1 [
"name" => "EVERITT R."
]
3 => array:1 [
"name" => "BOLAND A."
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 09:58:38"
"publicationUrl" => "https://link.springer.com/article/10.1007/s11222-014-9521-x"
"publicationInfo" => array:3 [
"pages" => "29-47"
"volume" => "26"
"number" => "1-2"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with tra "
"en" => "Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with transition kernel P such that π is invariant under P. However, there are many situations for which it is impractical or impossible to draw from the transition kernel P. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. Monte Carlo algorithms often aim to draw from a distribution π by simulating a Markov chain with tra "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
46 => Essec\Faculty\Model\Contribution {#2318
#_index: "academ_contributions"
#_id: "13901"
#_source: array:18 [
"id" => "13901"
"slug" => "13901-a-bayesian-approach-for-noisy-matrix-completion-optimal-rate-under-general-sampling-distribution 13901-a-bayesian-approach-for-noisy-matrix-completion-optimal-rate-under-general-sampling-distributi "
"yearMonth" => "2015-04"
"year" => "2015"
"title" => "A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution"
"description" => "MAI, T.T. et ALQUIER, P. (2015). A Bayesian approach for noisy matrix completion: Optimal rate under general sampling distribution. <i>The Electronic Journal of Statistics</i>, 9(1), pp. 823-841. MAI, T.T. et ALQUIER, P. (2015). A Bayesian approach for noisy matrix completion: Optimal rate under "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MAI The Tien"
]
]
"ouvrage" => ""
"keywords" => array:6 [
0 => "Matrix completion"
1 => "Bayesian Analysis"
2 => "PACBayesian bounds"
3 => "oracle inequality"
4 => "low-rank matrix"
5 => "Gibbs sampler"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-9/issue-1/A-Bayesian-approach-for-noisy-matrix-completion--Optimal-rate/10.1214/15-EJS1020.full https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-9/issue-1/A-Bayesian-appr "
"publicationInfo" => array:3 [
"pages" => "823-841"
"volume" => "9"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally [3, 18, 19, 24, 28]. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of view (see [7, 9, 16, 23] among others) in this problem, the theoretical optimality of Bayesian estimators have not been explored yet. In this paper, we propose a Bayesian estimator for matrix completion under general sampling distribution. We also provide an oracle inequality for this estimator. This inequality proves that, whatever the rank of the matrix to be estimated, our estimator reaches the minimax-optimal rate of convergence (up to a logarithmic factor). We end the paper with a short simulation study. Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient comp "
"en" => "Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient computationally [3, 18, 19, 24, 28]. While the behaviour of penalized minimization methods is well understood both from the theoretical and computational points of view (see [7, 9, 16, 23] among others) in this problem, the theoretical optimality of Bayesian estimators have not been explored yet. In this paper, we propose a Bayesian estimator for matrix completion under general sampling distribution. We also provide an oracle inequality for this estimator. This inequality proves that, whatever the rank of the matrix to be estimated, our estimator reaches the minimax-optimal rate of convergence (up to a logarithmic factor). We end the paper with a short simulation study. Bayesian methods for low-rank matrix completion with noise have been shown to be very efficient comp "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
47 => Essec\Faculty\Model\Contribution {#2319
#_index: "academ_contributions"
#_id: "13902"
#_source: array:18 [
"id" => "13902"
"slug" => "13902-pac-bayesian-auc-classification-and-scoring"
"yearMonth" => "2014-12"
"year" => "2014"
"title" => "PAC-Bayesian AUC Classification and Scoring"
"description" => "RIDGWAY, J., ALQUIER, P., CHOPIN, N. et LIANG, F. (2014). PAC-Bayesian AUC Classification and Scoring. Dans: <i>28th Conference on Neural Information Processing Systems (NIPS'14)</i>. Curran Associates, Inc. RIDGWAY, J., ALQUIER, P., CHOPIN, N. et LIANG, F. (2014). PAC-Bayesian AUC Classification and Scorin "
"authors" => array:4 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "RIDGWAY James"
]
2 => array:1 [
"name" => "CHOPIN Nicolas"
]
3 => array:1 [
"name" => "LIANG Feng"
]
]
"ouvrage" => "28th Conference on Neural Information Processing Systems (NIPS'14)"
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://papers.nips.cc/paper/5604-pac-bayesian-auc-classification-and-scoring"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
"abstract" => array:2 [
"fr" => "We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Area Under Curve) criterion. We focus initially on the class of linear score functions. We derive PAC-Bayesian non-asymptotic bounds for two types of prior for the score parameters: a Gaussian prior, and a spike-and-slab prior; the latter makes it possible to perform feature selection. One important advantage of our approach is that it is amenable to powerful Bayesian computational tools. We derive in particular a Sequential Monte Carlo algorithm, as an efficient method which may be used as a gold standard, and an Expectation-Propagation algorithm, as a much faster but approximate method. We also extend our method to a class of non-linear score functions, essentially leading to a nonparametric procedure, by considering a Gaussian process prior. We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Ar "
"en" => "We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Area Under Curve) criterion. We focus initially on the class of linear score functions. We derive PAC-Bayesian non-asymptotic bounds for two types of prior for the score parameters: a Gaussian prior, and a spike-and-slab prior; the latter makes it possible to perform feature selection. One important advantage of our approach is that it is amenable to powerful Bayesian computational tools. We derive in particular a Sequential Monte Carlo algorithm, as an efficient method which may be used as a gold standard, and an Expectation-Propagation algorithm, as a much faster but approximate method. We also extend our method to a class of non-linear score functions, essentially leading to a nonparametric procedure, by considering a Gaussian process prior. We develop a scoring and classification procedure based on the PAC-Bayesian approach and the AUC (Ar "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
48 => Essec\Faculty\Model\Contribution {#2320
#_index: "academ_contributions"
#_id: "13903"
#_source: array:18 [
"id" => "13903"
"slug" => "13903-prediction-of-time-series-by-statistical-learning-general-losses-and-fast-rates"
"yearMonth" => "2013-12"
"year" => "2013"
"title" => "Prediction of time series by statistical learning: general losses and fast rates"
"description" => "ALQUIER, P., LI, X. et WINTENBERGER, O. (2013). Prediction of time series by statistical learning: general losses and fast rates. <i>Dependence Modeling</i>, 1, pp. 65-93. ALQUIER, P., LI, X. et WINTENBERGER, O. (2013). Prediction of time series by statistical learning: g "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "LI Xiang"
]
2 => array:1 [
"name" => "WINTENBERGER Olivier"
]
]
"ouvrage" => ""
"keywords" => array:8 [
0 => "Statistical learning theory"
1 => "time series forecasting"
2 => "PAC-Bayesian bounds"
3 => "weak dependence"
4 => "mixing"
5 => "oracle inequalities"
6 => "fast rates"
7 => "GDP forecasting"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://www.degruyter.com/document/doi/10.2478/demo-2013-0004/html"
"publicationInfo" => array:3 [
"pages" => "65-93"
"volume" => "1"
"number" => null
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √d/n for the Gibbs estimator under the absolute loss were given in a previous work, where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the classical penalized ERM procedure. We apply this method for quantile forecasting of the French GDP. Under additional conditions on the loss functions (satisfied by the quadratic loss function) and for uniformly mixing processes, we prove that the Gibbs estimator actually achieves fast rates of convergence d/n. We discuss the optimality of these different rates pointing out references to lower bounds when they are available. In particular, these results bring a generalization the results of on sparse regression estimation to some auto regression. We establish rates of convergences in statistical learning for time series forecasting. Using the PA "
"en" => "We establish rates of convergences in statistical learning for time series forecasting. Using the PAC-Bayesian approach, slow rates of convergence √d/n for the Gibbs estimator under the absolute loss were given in a previous work, where n is the sample size and d the dimension of the set of predictors. Under the same weak dependence conditions, we extend this result to any convex Lipschitz loss function. We also identify a condition on the parameter space that ensures similar rates for the classical penalized ERM procedure. We apply this method for quantile forecasting of the French GDP. Under additional conditions on the loss functions (satisfied by the quadratic loss function) and for uniformly mixing processes, we prove that the Gibbs estimator actually achieves fast rates of convergence d/n. We discuss the optimality of these different rates pointing out references to lower bounds when they are available. In particular, these results bring a generalization the results of on sparse regression estimation to some auto regression. We establish rates of convergences in statistical learning for time series forecasting. Using the PA "
]
"authors_fields" => array:2 [
"fr" => "Management"
"en" => "Management"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
49 => Essec\Faculty\Model\Contribution {#2321
#_index: "academ_contributions"
#_id: "13904"
#_source: array:18 [
"id" => "13904"
"slug" => "13904-bayesian-methods-for-low-rank-matrix-estimation-short-survey-and-theoretical-study"
"yearMonth" => "2013-10"
"year" => "2013"
"title" => "Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study"
"description" => "ALQUIER, P. (2013). Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical Study. Dans: <i>24th International Conference on Algorithmic Learning Theory (ALT'13)</i>. Singapore: Springer Berlin Heidelberg, pp. 309-323. ALQUIER, P. (2013). Bayesian Methods for Low-Rank Matrix Estimation: Short Survey and Theoretical St "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "24th International Conference on Algorithmic Learning Theory (ALT'13)"
"keywords" => []
"updatedAt" => "2023-03-22 13:58:49"
"publicationUrl" => "https://link.springer.com/chapter/10.1007/978-3-642-40935-6_22"
"publicationInfo" => array:3 [
"pages" => "309-323"
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "he problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the different type of priors considered on matrices to favour low-rank. We also prove that the obtained Bayesian estimators, under suitable assumptions, enjoys the same optimality properties as the ones based on penalization. he problem of low-rank matrix estimation recently received a lot of attention due to challenging app "
"en" => "he problem of low-rank matrix estimation recently received a lot of attention due to challenging applications. A lot of work has been done on rank-penalized methods and convex relaxation, both on the theoretical and applied sides. However, only a few papers considered Bayesian estimation. In this paper, we review the different type of priors considered on matrices to favour low-rank. We also prove that the obtained Bayesian estimators, under suitable assumptions, enjoys the same optimality properties as the ones based on penalization. he problem of low-rank matrix estimation recently received a lot of attention due to challenging app "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
50 => Essec\Faculty\Model\Contribution {#2322
#_index: "academ_contributions"
#_id: "13905"
#_source: array:18 [
"id" => "13905"
"slug" => "13905-rank-penalized-estimation-of-a-quantum-system"
"yearMonth" => "2013-09"
"year" => "2013"
"title" => "Rank-penalized estimation of a quantum system"
"description" => "ALQUIER, P., BUTUCEA, C., HEBIRI, M., MEZIANI, K. et MORIMAE, T. (2013). Rank-penalized estimation of a quantum system. <i>Physical Review A</i>, 88(3). ALQUIER, P., BUTUCEA, C., HEBIRI, M., MEZIANI, K. et MORIMAE, T. (2013). Rank-penalized estimation o "
"authors" => array:5 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "BUTUCEA Cristina"
]
2 => array:1 [
"name" => "HEBIRI Mohamed"
]
3 => array:1 [
"name" => "MEZIANI Katia"
]
4 => array:1 [
"name" => "MORIMAE Tomoyuki"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 10:14:40"
"publicationUrl" => "https://journals.aps.org/pra/abstract/10.1103/PhysRevA.88.032113"
"publicationInfo" => array:3 [
"pages" => ""
"volume" => "88"
"number" => "3"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We introduce a method to reconstruct the density matrix ρ of a system of n qubits and estimate its rank d from data obtained by quantum-state-tomography measurements repeated m times. The procedure consists of minimizing the risk of a linear estimator ˆρ of ρ penalized by a given rank (from 1 to 2n), where ˆρ is previously obtained by the moment method. We obtain simultaneously an estimator of the rank and the resulting density matrix associated to this rank. We establish an upper bound for the error of the penalized estimator, evaluated with the Frobenius norm, which is of order dn(4/3)n/m and consistent for the estimator of the rank. The proposed methodology is computationally efficient and is illustrated with some example states and real experimental data sets. We introduce a method to reconstruct the density matrix ρ of a system of n qubits and estimate its r "
"en" => "We introduce a method to reconstruct the density matrix ρ of a system of n qubits and estimate its rank d from data obtained by quantum-state-tomography measurements repeated m times. The procedure consists of minimizing the risk of a linear estimator ˆρ of ρ penalized by a given rank (from 1 to 2n), where ˆρ is previously obtained by the moment method. We obtain simultaneously an estimator of the rank and the resulting density matrix associated to this rank. We establish an upper bound for the error of the penalized estimator, evaluated with the Frobenius norm, which is of order dn(4/3)n/m and consistent for the estimator of the rank. The proposed methodology is computationally efficient and is illustrated with some example states and real experimental data sets. We introduce a method to reconstruct the density matrix ρ of a system of n qubits and estimate its r "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
51 => Essec\Faculty\Model\Contribution {#2323
#_index: "academ_contributions"
#_id: "13906"
#_source: array:18 [
"id" => "13906"
"slug" => "13906-adaptive-estimation-of-the-density-matrix-in-quantum-homodyne-tomography-with-noisy-data"
"yearMonth" => "2013-06"
"year" => "2013"
"title" => "Adaptive estimation of the density matrix in quantum homodyne tomography with noisy data"
"description" => "ALQUIER, P., MEZIANI, K. et PEYRÉ, G. (2013). Adaptive estimation of the density matrix in quantum homodyne tomography with noisy data. <i>Inverse Problems</i>, 29(7), pp. 075017. ALQUIER, P., MEZIANI, K. et PEYRÉ, G. (2013). Adaptive estimation of the density matrix in quantum h "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "MEZIANI K"
]
2 => array:1 [
"name" => "PEYRÉ G"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 10:16:12"
"publicationUrl" => "https://iopscience.iop.org/article/10.1088/0266-5611/29/7/075017/meta"
"publicationInfo" => array:3 [
"pages" => "075017"
"volume" => "29"
"number" => "7"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
52 => Essec\Faculty\Model\Contribution {#2324
#_index: "academ_contributions"
#_id: "13907"
#_source: array:18 [
"id" => "13907"
"slug" => "13907-sparse-single-index-model"
"yearMonth" => "2013-01"
"year" => "2013"
"title" => "Sparse Single-Index Model"
"description" => "ALQUIER, P. et BIAU, G. (2013). Sparse Single-Index Model. <i>Journal of Machine Learning Research</i>, 14, pp. 243-280. ALQUIER, P. et BIAU, G. (2013). Sparse Single-Index Model. <i>Journal of Machine Learning Research</ "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "BIAU Gérard"
]
]
"ouvrage" => ""
"keywords" => array:6 [
0 => "single-index model"
1 => "sparsity"
2 => "regression estimation"
3 => "PAC-Bayesian"
4 => "oracle inequality"
5 => "reversible jump Markov chain Monte Carlo method"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://jmlr.csail.mit.edu/papers/v14/alquier13a.html"
"publicationInfo" => array:3 [
"pages" => "243-280"
"volume" => "14"
"number" => null
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
"abstract" => array:2 [
"fr" => "We consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesian approach. On the theoretical side, we offer a sharp oracle inequality, which is more powerful than the best known oracle inequalities for other common procedures of single-index recovery. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technique and its performance is compared with that of standard procedures. We consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesi "
"en" => "We consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesian approach. On the theoretical side, we offer a sharp oracle inequality, which is more powerful than the best known oracle inequalities for other common procedures of single-index recovery. The proposed method is implemented by means of the reversible jump Markov chain Monte Carlo technique and its performance is compared with that of standard procedures. We consider the single-index model estimation problem from a sparsity perspective using a PAC-Bayesi "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
53 => Essec\Faculty\Model\Contribution {#2325
#_index: "academ_contributions"
#_id: "13908"
#_source: array:18 [
"id" => "13908"
"slug" => "13908-pac-bayesian-estimation-and-prediction-in-sparse-additive-models"
"yearMonth" => "2013-01"
"year" => "2013"
"title" => "PAC-Bayesian estimation and prediction in sparse additive models"
"description" => "GUEDJ, B. et ALQUIER, P. (2013). PAC-Bayesian estimation and prediction in sparse additive models. <i>The Electronic Journal of Statistics</i>, 7, pp. 264-291. GUEDJ, B. et ALQUIER, P. (2013). PAC-Bayesian estimation and prediction in sparse additive models. < "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "GUEDJ Benjamin"
]
]
"ouvrage" => ""
"keywords" => array:7 [
0 => "Additive models"
1 => "MCMC"
2 => "Oracle inequality"
3 => "PAC-Bayesian bounds"
4 => "Regression estimation"
5 => "Sparsity"
6 => "stochastic search"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-7/issue-none/PAC-Bayesian-estimation-and-prediction-in-sparse-additive-models/10.1214/13-EJS771.full https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-7/issue-none/PAC-Bayesian "
"publicationInfo" => array:3 [
"pages" => "264-291"
"volume" => "7"
"number" => null
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "The present paper is about estimation and prediction in high-dimensional additive models under a sparsity assumption (p ≫ n paradigm). A PAC-Bayesian strategy is investigated, delivering oracle inequalities in probability. The implementation is performed through recent outcomes in high-dimensional MCMC algorithms, and the performance of our method is assessed on simulated data. The present paper is about estimation and prediction in high-dimensional additive models under a spa "
"en" => "The present paper is about estimation and prediction in high-dimensional additive models under a sparsity assumption (p ≫ n paradigm). A PAC-Bayesian strategy is investigated, delivering oracle inequalities in probability. The implementation is performed through recent outcomes in high-dimensional MCMC algorithms, and the performance of our method is assessed on simulated data. The present paper is about estimation and prediction in high-dimensional additive models under a spa "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
54 => Essec\Faculty\Model\Contribution {#2326
#_index: "academ_contributions"
#_id: "13909"
#_source: array:18 [
"id" => "13909"
"slug" => "13909-prediction-of-quantiles-by-statistical-learning-and-application-to-gdp-forecasting"
"yearMonth" => "2012-10"
"year" => "2012"
"title" => "Prediction of Quantiles by Statistical Learning and Application to GDP Forecasting"
"description" => "ALQUIER, P. et LI, X. (2012). Prediction of Quantiles by Statistical Learning and Application to GDP Forecasting. Dans: <i>15th International Conference on Discovery Science (DS'12)</i>. Lyon: Springer Berlin Heidelberg, pp. 22-36. ALQUIER, P. et LI, X. (2012). Prediction of Quantiles by Statistical Learning and Application to GDP "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "LI Xiang"
]
]
"ouvrage" => "15th International Conference on Discovery Science (DS'12)"
"keywords" => []
"updatedAt" => "2023-03-22 13:57:13"
"publicationUrl" => "https://link.springer.com/chapter/10.1007/978-3-642-33492-4_5"
"publicationInfo" => array:3 [
"pages" => "22-36"
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "n this paper, we tackle the problem of prediction and confidence intervals for time series using a statistical learning approach and quantile loss functions. In a first time, we show that the Gibbs estimator is able to predict as well as the best predictor in a given family for a wide set of loss functions. In particular, using the quantile loss function of [1], this allows to build confidence intervals. We apply these results to the problem of prediction and confidence regions for the French Gross Domestic Product (GDP) growth, with promising results. n this paper, we tackle the problem of prediction and confidence intervals for time series using a s "
"en" => "n this paper, we tackle the problem of prediction and confidence intervals for time series using a statistical learning approach and quantile loss functions. In a first time, we show that the Gibbs estimator is able to predict as well as the best predictor in a given family for a wide set of loss functions. In particular, using the quantile loss function of [1], this allows to build confidence intervals. We apply these results to the problem of prediction and confidence regions for the French Gross Domestic Product (GDP) growth, with promising results. n this paper, we tackle the problem of prediction and confidence intervals for time series using a s "
]
"authors_fields" => array:2 [
"fr" => "Management"
"en" => "Management"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
55 => Essec\Faculty\Model\Contribution {#2327
#_index: "academ_contributions"
#_id: "13910"
#_source: array:18 [
"id" => "13910"
"slug" => "13910-model-selection-for-weakly-dependent-time-series-forecasting"
"yearMonth" => "2012-08"
"year" => "2012"
"title" => "Model selection for weakly dependent time series forecasting"
"description" => "ALQUIER, P. et WINTENBERGER, O. (2012). Model selection for weakly dependent time series forecasting. <i>Bernoulli: A Journal of Mathematical Statistics and Probability</i>, 18(3), pp. 883-913. ALQUIER, P. et WINTENBERGER, O. (2012). Model selection for weakly dependent time series forecasting "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "WINTENBERGER Olivier"
]
]
"ouvrage" => ""
"keywords" => array:8 [
0 => "adaptative inference"
1 => "aggregation of estimators"
2 => "autoregression estimation"
3 => "model selection"
4 => "randomized estimators"
5 => "statistical learning"
6 => "time series prediction"
7 => "weak dependence"
]
"updatedAt" => "2023-03-22 10:26:35"
"publicationUrl" => "https://projecteuclid.org/journals/bernoulli/volume-18/issue-3/Model-selection-for-weakly-dependent-time-series-forecasting/10.3150/11-BEJ359.full https://projecteuclid.org/journals/bernoulli/volume-18/issue-3/Model-selection-for-weakly-dependent- "
"publicationInfo" => array:3 [
"pages" => "883-913"
"volume" => "18"
"number" => "3"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Observing a stationary time series, we propose a two-steps procedure for the prediction of its next value. The first step follows machine learning theory paradigm and consists in determining a set of possible predictors as randomized estimators in (possibly numerous) different predictive models. The second step follows the model selection paradigm and consists in choosing one predictor with good properties among all the predictors of the first step. We study our procedure for two different types of observations: causal Bernoulli shifts and bounded weakly dependent processes. In both cases, we give oracle inequalities: the risk of the chosen predictor is close to the best prediction risk in all predictive models that we consider. We apply our procedure for predictive models as linear predictors, neural networks predictors and nonparametric autoregressive predictors. Observing a stationary time series, we propose a two-steps procedure for the prediction of its next "
"en" => "Observing a stationary time series, we propose a two-steps procedure for the prediction of its next value. The first step follows machine learning theory paradigm and consists in determining a set of possible predictors as randomized estimators in (possibly numerous) different predictive models. The second step follows the model selection paradigm and consists in choosing one predictor with good properties among all the predictors of the first step. We study our procedure for two different types of observations: causal Bernoulli shifts and bounded weakly dependent processes. In both cases, we give oracle inequalities: the risk of the chosen predictor is close to the best prediction risk in all predictive models that we consider. We apply our procedure for predictive models as linear predictors, neural networks predictors and nonparametric autoregressive predictors. Observing a stationary time series, we propose a two-steps procedure for the prediction of its next "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
56 => Essec\Faculty\Model\Contribution {#2328
#_index: "academ_contributions"
#_id: "13911"
#_source: array:18 [
"id" => "13911"
"slug" => "13911-transductive-versions-of-the-lasso-and-the-dantzig-selector"
"yearMonth" => "2012-09"
"year" => "2012"
"title" => "Transductive versions of the LASSO and the Dantzig Selector"
"description" => "ALQUIER, P. et HEBIRI, M. (2012). Transductive versions of the LASSO and the Dantzig Selector. <i>Journal of Statistical Planning and Inference</i>, 142(9), pp. 2485-2500. ALQUIER, P. et HEBIRI, M. (2012). Transductive versions of the LASSO and the Dantzig Selector. <i>Jo "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "HEBIRI Mohamed"
]
]
"ouvrage" => ""
"keywords" => array:6 [
0 => "High-dimensional data"
1 => "LASSO"
2 => "Sparsity"
3 => "High-dimensional regression estimation"
4 => "Variable selection"
5 => "Transduction"
]
"updatedAt" => "2023-03-22 10:24:37"
"publicationUrl" => "https://www.sciencedirect.com/science/article/pii/S037837581200136X"
"publicationInfo" => array:3 [
"pages" => "2485-2500"
"volume" => "142"
"number" => "9"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing transductive prediction procedures that are able to take advantage of the sparsity in the high dimensional linear regression. More precisely, we define transductive versions of the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candès and Tao, 2007). These procedures combine labeled and unlabeled observations of the training dataset to produce a prediction for the unlabeled observations. We propose an experimental study of the transductive estimators that shows that they improve the LASSO and Dantzig Selector in many situations, and particularly in high dimensional problems when the predictors are correlated. We then provide non-asymptotic theoretical guarantees for these estimation methods. Interestingly, our theoretical results show that the Transductive LASSO and Dantzig Selector satisfy sparsity inequalities under weaker assumptions than those required for the “original” LASSO. Transductive methods are useful in prediction problems when the training dataset is composed of a la "
"en" => "Transductive methods are useful in prediction problems when the training dataset is composed of a large number of unlabeled observations and a smaller number of labeled observations. In this paper, we propose an approach for developing transductive prediction procedures that are able to take advantage of the sparsity in the high dimensional linear regression. More precisely, we define transductive versions of the LASSO (Tibshirani, 1996) and the Dantzig Selector (Candès and Tao, 2007). These procedures combine labeled and unlabeled observations of the training dataset to produce a prediction for the unlabeled observations. We propose an experimental study of the transductive estimators that shows that they improve the LASSO and Dantzig Selector in many situations, and particularly in high dimensional problems when the predictors are correlated. We then provide non-asymptotic theoretical guarantees for these estimation methods. Interestingly, our theoretical results show that the Transductive LASSO and Dantzig Selector satisfy sparsity inequalities under weaker assumptions than those required for the “original” LASSO. Transductive methods are useful in prediction problems when the training dataset is composed of a la "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
57 => Essec\Faculty\Model\Contribution {#2329
#_index: "academ_contributions"
#_id: "13912"
#_source: array:18 [
"id" => "13912"
"slug" => "13912-generalization-of-constraints-for-high-dimensional-regression-problems"
"yearMonth" => "2011-12"
"year" => "2011"
"title" => "Generalization of constraints for high dimensional regression problems"
"description" => "ALQUIER, P. et HEBIRI, M. (2011). Generalization of constraints for high dimensional regression problems. <i>Statistics & Probability Letters</i>, 81(12), pp. 1760-1765. ALQUIER, P. et HEBIRI, M. (2011). Generalization of constraints for high dimensional regression prob "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "HEBIRI Mohamed"
]
]
"ouvrage" => ""
"keywords" => array:5 [
0 => "High-dimensional data"
1 => "LASSO"
2 => "Restricted eigenvalue assumption"
3 => "Sparsity"
4 => "Variable selection"
]
"updatedAt" => "2023-03-22 12:07:29"
"publicationUrl" => "https://www.sciencedirect.com/science/article/pii/S0167715211002422"
"publicationInfo" => array:3 [
"pages" => "1760-1765"
"volume" => "81"
"number" => "12"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
58 => Essec\Faculty\Model\Contribution {#2330
#_index: "academ_contributions"
#_id: "13913"
#_source: array:18 [
"id" => "13913"
"slug" => "13913-sparsity-considerations-for-dependent-variables"
"yearMonth" => "2011-08"
"year" => "2011"
"title" => "Sparsity considerations for dependent variables"
"description" => "ALQUIER, P. et DOUKHAN, P. (2011). Sparsity considerations for dependent variables. <i>The Electronic Journal of Statistics</i>, 5, pp. 750-774. ALQUIER, P. et DOUKHAN, P. (2011). Sparsity considerations for dependent variables. <i>The Electroni "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "DOUKHAN Paul"
]
]
"ouvrage" => ""
"keywords" => array:8 [
0 => "Density estimation"
1 => "deviation of empirical mean"
2 => "Estimation in high dimension"
3 => "Lasso"
4 => "Penalization"
5 => "Regression estimation"
6 => "Sparsity"
7 => "Weak dependence"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-5/issue-none/Sparsity-considerations-for-dependent-variables/10.1214/11-EJS626.full https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-5/issue-none/Sparsity-con "
"publicationInfo" => array:3 [
"pages" => "750-774"
"volume" => "5"
"number" => null
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "The aim of this paper is to provide a comprehensive introduction for the study of ℓ1-penalized estimators in the context of dependent observations. We define a general ℓ1-penalized estimator for solving problems of stochastic optimization. This estimator turns out to be the LASSO [Tib96] in the regression estimation setting. Powerful theoretical guarantees on the statistical performances of the LASSO were provided in recent papers, however, they usually only deal with the iid case. Here, we study this estimator under various dependence assumptions. The aim of this paper is to provide a comprehensive introduction for the study of ℓ1-penalized estim "
"en" => "The aim of this paper is to provide a comprehensive introduction for the study of ℓ1-penalized estimators in the context of dependent observations. We define a general ℓ1-penalized estimator for solving problems of stochastic optimization. This estimator turns out to be the LASSO [Tib96] in the regression estimation setting. Powerful theoretical guarantees on the statistical performances of the LASSO were provided in recent papers, however, they usually only deal with the iid case. Here, we study this estimator under various dependence assumptions. The aim of this paper is to provide a comprehensive introduction for the study of ℓ1-penalized estim "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
59 => Essec\Faculty\Model\Contribution {#2331
#_index: "academ_contributions"
#_id: "13914"
#_source: array:18 [
"id" => "13914"
"slug" => "13914-pac-bayesian-bounds-for-sparse-regression-estimation-with-exponential-weights"
"yearMonth" => "2011-03"
"year" => "2011"
"title" => "PAC-Bayesian bounds for sparse regression estimation with exponential weights"
"description" => "ALQUIER, P. et LOUNICI, K. (2011). PAC-Bayesian bounds for sparse regression estimation with exponential weights. <i>The Electronic Journal of Statistics</i>, 5, pp. 127-145. ALQUIER, P. et LOUNICI, K. (2011). PAC-Bayesian bounds for sparse regression estimation with exponen "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "LOUNICI Karim"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "Exponential weights"
1 => "high-dimensional regression"
2 => "PAC-Bayesian inequalities"
3 => "Sparsity oracle inequality"
]
"updatedAt" => "2023-03-22 12:55:44"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-5/issue-none/PAC-Bayesian-bounds-for-sparse-regression-estimation-with-exponential-weights/10.1214/11-EJS601.full https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-5/issue-none/PAC-Bayesian "
"publicationInfo" => array:3 [
"pages" => "127-145"
"volume" => "5"
"number" => ""
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We consider the sparse regression model where the number of parameters p is larger than the sample size n. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between statistical and computational performances. The Lasso is solution of a convex minimization problem, hence computable for large value of p. However stringent conditions on the design are required to establish fast rates of convergence for this estimator. Dalalyan and Tsybakov proposed an exponential weights procedure achieving a good compromise between the statistical and computational aspects. This estimator can be computed for reasonably large p and satisfies a sparsity oracle inequality in expectation for the empirical excess risk only under mild assumptions on the design. We consider the sparse regression model where the number of parameters p is larger than the sample s "
"en" => "We consider the sparse regression model where the number of parameters p is larger than the sample size n. The difficulty when considering high-dimensional problems is to propose estimators achieving a good compromise between statistical and computational performances. The Lasso is solution of a convex minimization problem, hence computable for large value of p. However stringent conditions on the design are required to establish fast rates of convergence for this estimator. Dalalyan and Tsybakov proposed an exponential weights procedure achieving a good compromise between the statistical and computational aspects. This estimator can be computed for reasonably large p and satisfies a sparsity oracle inequality in expectation for the empirical excess risk only under mild assumptions on the design. We consider the sparse regression model where the number of parameters p is larger than the sample s "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
60 => Essec\Faculty\Model\Contribution {#2332
#_index: "academ_contributions"
#_id: "13915"
#_source: array:18 [
"id" => "13915"
"slug" => "13915-an-algorithm-for-iterative-selection-of-blocks-of-features"
"yearMonth" => "2010-10"
"year" => "2010"
"title" => "An Algorithm for Iterative Selection of Blocks of Features"
"description" => "ALQUIER, P. (2010). An Algorithm for Iterative Selection of Blocks of Features. Dans: <i>21st International Conference on Algorithmic Learning Theory (ALT'10)</i>. Caberra: Springer Berlin Heidelberg, pp. 35-49. ALQUIER, P. (2010). An Algorithm for Iterative Selection of Blocks of Features. Dans: <i>21st Intern "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "21st International Conference on Algorithmic Learning Theory (ALT'10)"
"keywords" => array:5 [
0 => "Feature Selection"
1 => "Sparsity"
2 => "Linear Regression"
3 => "Grouped Variables"
4 => "ArrayCGH"
]
"updatedAt" => "2023-03-22 13:10:17"
"publicationUrl" => "https://link.springer.com/chapter/10.1007/978-3-642-16108-7_7"
"publicationInfo" => array:3 [
"pages" => "35-49"
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We focus on the problem of linear regression estimation in high dimension, when the parameter β is ”sparse” (most of its coordinates are 0) and ”blocky” (β i and β i + 1 are likely to be equal). Recently, some authors defined estimators taking into account this information, such as the Fused-LASSO [19] or the S-LASSO among others. However, there are no theoretical results about the obtained estimators in the general design matrix case. Here, we propose an alternative point of view, based on the Iterative Feature Selection method. We propose an iterative algorithm that takes into account the fact that β is sparse and blocky, with no prior knowledge on the position of the blocks. Moreover, we give a theoretical result that ensures that every step of our algorithm actually improves the statistical performance of the obtained estimator. We provide some simulations, where our method outperforms LASSO-type methods in the cases where the parameter is sparse and blocky. Moreover, we give an application to real data (CGH arrays), that shows that our estimator can be used on large datasets. We focus on the problem of linear regression estimation in high dimension, when the parameter β is ” "
"en" => "We focus on the problem of linear regression estimation in high dimension, when the parameter β is ”sparse” (most of its coordinates are 0) and ”blocky” (β i and β i + 1 are likely to be equal). Recently, some authors defined estimators taking into account this information, such as the Fused-LASSO [19] or the S-LASSO among others. However, there are no theoretical results about the obtained estimators in the general design matrix case. Here, we propose an alternative point of view, based on the Iterative Feature Selection method. We propose an iterative algorithm that takes into account the fact that β is sparse and blocky, with no prior knowledge on the position of the blocks. Moreover, we give a theoretical result that ensures that every step of our algorithm actually improves the statistical performance of the obtained estimator. We provide some simulations, where our method outperforms LASSO-type methods in the cases where the parameter is sparse and blocky. Moreover, we give an application to real data (CGH arrays), that shows that our estimator can be used on large datasets. We focus on the problem of linear regression estimation in high dimension, when the parameter β is ” "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
61 => Essec\Faculty\Model\Contribution {#2333
#_index: "academ_contributions"
#_id: "13916"
#_source: array:18 [
"id" => "13916"
"slug" => "13916-pac-bayesian-bounds-for-randomized-empirical-risk-minimizers"
"yearMonth" => "2008-12"
"year" => "2008"
"title" => "PAC-Bayesian bounds for randomized empirical risk minimizers"
"description" => "ALQUIER, P. (2008). PAC-Bayesian bounds for randomized empirical risk minimizers. <i>Mathematical Methods of Statistics</i>, 17(4), pp. 279-304. ALQUIER, P. (2008). PAC-Bayesian bounds for randomized empirical risk minimizers. <i>Mathematical Me "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-03-22 12:57:14"
"publicationUrl" => "https://link.springer.com/article/10.3103/S1066530708040017"
"publicationInfo" => array:3 [
"pages" => "279-304"
"volume" => "17"
"number" => "4"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control of the risk of the latter. These results allow us to bound the risk of very general estimation procedures, as well as to perform model selection. The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] in the clas "
"en" => "The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] in the classification setting to more general problems of statistical inference. We show how to control the deviations of the risk of randomized estimators. A particular attention is paid to randomized estimators drawn in a small neighborhood of classical estimators, whose study leads to control of the risk of the latter. These results allow us to bound the risk of very general estimation procedures, as well as to perform model selection. The aim of this paper is to generalize the PAC-Bayesian theorems proved by Catoni [6, 8] in the clas "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
62 => Essec\Faculty\Model\Contribution {#2334
#_index: "academ_contributions"
#_id: "13917"
#_source: array:18 [
"id" => "13917"
"slug" => "13917-lasso-iterative-feature-selection-and-the-correlation-selector-oracle-inequalities-and-numerical-performances 13917-lasso-iterative-feature-selection-and-the-correlation-selector-oracle-inequalities-and-numeric "
"yearMonth" => "2008-11"
"year" => "2008"
"title" => "LASSO, Iterative Feature Selection and the Correlation Selector: Oracle inequalities and numerical performances LASSO, Iterative Feature Selection and the Correlation Selector: Oracle inequalities and numerical p "
"description" => "ALQUIER, P. (2008). LASSO, Iterative Feature Selection and the Correlation Selector: Oracle inequalities and numerical performances. <i>The Electronic Journal of Statistics</i>, 2, pp. 1129-1152. ALQUIER, P. (2008). LASSO, Iterative Feature Selection and the Correlation Selector: Oracle inequali "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:5 [
0 => "Confidence regions"
1 => "Lasso"
2 => "Regression estimation"
3 => "shrinkage and thresholding methods"
4 => "Statistical learning"
]
"updatedAt" => "2023-03-22 12:59:39"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-2/issue-none/LASSO-Iterative-Feature-Selection-and-the-Correlation-Selector--Oracle/10.1214/08-EJS288.full https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-2/issue-none/LASSO-Iterat "
"publicationInfo" => array:3 [
"pages" => "1129-1152"
"volume" => "2"
"number" => ""
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We propose a general family of algorithms for regression estimation with quadratic loss, on the basis of geometrical considerations. These algorithms are able to select relevant functions into a large dictionary. We prove that a lot of methods that have already been studied for this task (LASSO, Dantzig selector, Iterative Feature Selection, among others) belong to our family, and exhibit another particular member of this family that we call Correlation Selector in this paper. Using general properties of our family of algorithm we prove oracle inequalities for IFS, for the LASSO and for the Correlation Selector, and compare numerical performances of these estimators on a toy example. We propose a general family of algorithms for regression estimation with quadratic loss, on the basi "
"en" => "We propose a general family of algorithms for regression estimation with quadratic loss, on the basis of geometrical considerations. These algorithms are able to select relevant functions into a large dictionary. We prove that a lot of methods that have already been studied for this task (LASSO, Dantzig selector, Iterative Feature Selection, among others) belong to our family, and exhibit another particular member of this family that we call Correlation Selector in this paper. Using general properties of our family of algorithm we prove oracle inequalities for IFS, for the LASSO and for the Correlation Selector, and compare numerical performances of these estimators on a toy example. We propose a general family of algorithms for regression estimation with quadratic loss, on the basi "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
63 => Essec\Faculty\Model\Contribution {#2335
#_index: "academ_contributions"
#_id: "13918"
#_source: array:18 [
"id" => "13918"
"slug" => "13918-density-estimation-with-quadratic-loss-a-confidence-intervals-method"
"yearMonth" => "2008-07"
"year" => "2008"
"title" => "Density estimation with quadratic loss: a confidence intervals method"
"description" => "ALQUIER, P. (2008). Density estimation with quadratic loss: a confidence intervals method. <i>ESAIM: Probability and Statistics</i>, 12, pp. 438-463. ALQUIER, P. (2008). Density estimation with quadratic loss: a confidence intervals method. <i>ESAIM: "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:5 [
0 => "Density estimation"
1 => "support vector machines"
2 => "kernel algorithms"
3 => "thresholding methods"
4 => "wavelets"
]
"updatedAt" => "2023-03-22 13:04:08"
"publicationUrl" => "https://doi.org/10.1051/ps:2007050"
"publicationInfo" => array:3 [
"pages" => "438-463"
"volume" => "12"
"number" => ""
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case where features are defined by wavelets, we prove that this method is adaptative near minimax (up to a log term) in some Besov spaces. We end the paper by simulations indicating that it must be possible to extend the adaptation result to other features We propose a feature selection method for density estimation with quadratic loss. This method relies "
"en" => "We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case where features are defined by wavelets, we prove that this method is adaptative near minimax (up to a log term) in some Besov spaces. We end the paper by simulations indicating that it must be possible to extend the adaptation result to other features We propose a feature selection method for density estimation with quadratic loss. This method relies "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
64 => Essec\Faculty\Model\Contribution {#2336
#_index: "academ_contributions"
#_id: "13919"
#_source: array:18 [
"id" => "13919"
"slug" => "13919-iterative-feature-selection-in-least-square-regression-estimation"
"yearMonth" => "2008-02"
"year" => "2008"
"title" => "Iterative feature selection in least square regression estimation"
"description" => "ALQUIER, P. (2008). Iterative feature selection in least square regression estimation. <i>Annales de l Institut Henri Poincare-Probabilites et Statistiques</i>, 44(1), pp. 47-88. ALQUIER, P. (2008). Iterative feature selection in least square regression estimation. <i>Annales de "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:5 [
0 => "Confidence regions"
1 => "Regression estimation"
2 => "Statistical learning"
3 => "Support vector machines"
4 => "Thresholding methods"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://projecteuclid.org/journals/annales-de-linstitut-henri-poincare-probabilites-et-statistiques/volume-44/issue-1/Iterative-feature-selection-in-least-square-regression-estimation/10.1214/07-AIHP106.full https://projecteuclid.org/journals/annales-de-linstitut-henri-poincare-probabilites-et-statistiques/ "
"publicationInfo" => array:3 [
"pages" => "47-88"
"volume" => "44"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Cette article présente un nouvel algorithme d’estimation de régression, dans les contextes inductifs et transductifs. L’estimateur est défini par une combinaison linéaire de fonctions choisies dans un dictionnaire donné. Les coefficients de cette combinaison sont calculés par des projections successives sur des ensembles simples. Ces ensembles sont définis comme des régions de confiance données par une inégalité de déviation (ou inégalité PAC). On démontre en particulier que chaque projection au cours de l’algorithme améliore effectivement l’estimateur obtenu. On donne tout d’abord les résultats dans le contexte inductif, où l’algorithme nécessite la connaissance de la distribution du design, puis dans le contexte transductif, plus naturel ici puisque l’algorithme s’applique sans la connaissance de cette distribution. On établit finalement un lien avec les inégalités d’oracle, permettant de montrer que notre estimateur atteint les vitesses optimales dans les espaces de Sobolev et de Besov. Cette article présente un nouvel algorithme d’estimation de régression, dans les contextes inductifs "
"en" => "This paper presents a new algorithm to perform regression estimation, in both the inductive and transductive setting. The estimator is defined as a linear combination of functions in a given dictionary. Coefficients of the combinations are computed sequentially using projection on some simple sets. These sets are defined as confidence regions provided by a deviation (PAC) inequality on an estimator in one-dimensional models. We prove that every projection the algorithm actually improves the performance of the estimator. We give all the estimators and results at first in the inductive case, where the algorithm requires the knowledge of the distribution of the design, and then in the transductive case, which seems a more natural application for this algorithm as we do not need particular information on the distribution of the design in this case. We finally show a connection with oracle inequalities, making us able to prove that the estimator reaches minimax rates of convergence in Sobolev and Besov spaces. This paper presents a new algorithm to perform regression estimation, in both the inductive and tran "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
65 => Essec\Faculty\Model\Contribution {#2337
#_index: "academ_contributions"
#_id: "13920"
#_source: array:18 [
"id" => "13920"
"slug" => "13920-constributions-to-statistical-learning-in-sparse-models"
"yearMonth" => "2013-12"
"year" => "2013"
"title" => "Constributions to Statistical Learning in Sparse Models"
"description" => "ALQUIER, P. (2013). Constributions to Statistical Learning in Sparse Models. Paris: France."
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "http://tel.archives-ouvertes.fr/tel-00915505"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "HDR"
"en" => "HDR"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "The aim of this habilitation thesis is to give an overview of my works on high-dimensional statistics and statistical learning, under various sparsity assumptions. In a first part, I will describe the major challenges of high-dimensional statistics in the context of the generic linear regression model. After a brief review of existing results, I will present the theoretical study of aggregated estimators that was done in (Alquier & Lounici 2011). The second part essentially aims at providing extensions of the various theories presented in the first part to the estimation of time series models (Alquier & Doukhan 2011, Alquier & Wintenberger 2013, Alquier & Li 2012, Alquier, Wintenberger & Li 2012). Finally, the third part presents various extensions to nonparametric models, or to specific applications such as quantum statistics (Alquier & Biau 2013, Guedj & Alquier 2013, Alquier, Meziani & Peyré 2013, Alquier, Butucea, Hebiri, Meziani & Morimae 2013, Alquier 2013, Alquier 2008). In each section, we provide explicitely the estimators used and, as much as possible, optimal oracle inequalities satisfied by these estimators. The aim of this habilitation thesis is to give an overview of my works on high-dimensional statistic "
"en" => "The aim of this habilitation thesis is to give an overview of my works on high-dimensional statistics and statistical learning, under various sparsity assumptions. In a first part, I will describe the major challenges of high-dimensional statistics in the context of the generic linear regression model. After a brief review of existing results, I will present the theoretical study of aggregated estimators that was done in (Alquier & Lounici 2011). The second part essentially aims at providing extensions of the various theories presented in the first part to the estimation of time series models (Alquier & Doukhan 2011, Alquier & Wintenberger 2013, Alquier & Li 2012, Alquier, Wintenberger & Li 2012). Finally, the third part presents various extensions to nonparametric models, or to specific applications such as quantum statistics (Alquier & Biau 2013, Guedj & Alquier 2013, Alquier, Meziani & Peyré 2013, Alquier, Butucea, Hebiri, Meziani & Morimae 2013, Alquier 2013, Alquier 2008). In each section, we provide explicitely the estimators used and, as much as possible, optimal oracle inequalities satisfied by these estimators. The aim of this habilitation thesis is to give an overview of my works on high-dimensional statistic "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
66 => Essec\Faculty\Model\Contribution {#2338
#_index: "academ_contributions"
#_id: "13976"
#_source: array:18 [
"id" => "13976"
"slug" => "13976-estimation-of-copulas-via-maximum-mean-discrepancy"
"yearMonth" => "2023-07"
"year" => "2023"
"title" => "Estimation of Copulas via Maximum Mean Discrepancy"
"description" => "ALQUIER, P., CHERIEF-ABDELLATIF, B.E., DERUMIGNY, A. et FERMANIAN, J.D. (2023). Estimation of Copulas via Maximum Mean Discrepancy. <i>Journal of the American Statistical Association</i>, 118(543), pp. 1997-2012. ALQUIER, P., CHERIEF-ABDELLATIF, B.E., DERUMIGNY, A. et FERMANIAN, J.D. (2023). Estimation of Copula "
"authors" => array:4 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:2 [
"name" => "CHERIEF-ABDELLATIF Badr-Eddine"
"bid" => "B00810114"
]
2 => array:1 [
"name" => "DERUMIGNY Alexis"
]
3 => array:1 [
"name" => "FERMANIAN Jean-David"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "Algorithms semiparametric inference"
1 => "Copula"
2 => "Kernel methods and RKHS"
3 => "Robust procedures"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1080/01621459.2021.2024836"
"publicationInfo" => array:3 [
"pages" => "1997-2012"
"volume" => "118"
"number" => "543"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "This article deals with robust inference for parametric copula models. Estimation using canonical maximum likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the maximum mean discrepancy (MMD) principle. We derive nonasymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. This article deals with robust inference for parametric copula models. Estimation using canonical ma "
"en" => "This article deals with robust inference for parametric copula models. Estimation using canonical maximum likelihood might be unstable, especially in the presence of outliers. We propose to use a procedure based on the maximum mean discrepancy (MMD) principle. We derive nonasymptotic oracle inequalities, consistency and asymptotic normality of this new estimator. In particular, the oracle inequality holds without any assumption on the copula family, and can be applied in the presence of outliers or under misspecification. This article deals with robust inference for parametric copula models. Estimation using canonical ma "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
67 => Essec\Faculty\Model\Contribution {#2339
#_index: "academ_contributions"
#_id: "13980"
#_source: array:18 [
"id" => "13980"
"slug" => "13980-universal-robust-regression-via-maximum-mean-discrepancy"
"yearMonth" => "2024-02"
"year" => "2024"
"title" => "Universal Robust Regression via Maximum Mean Discrepancy"
"description" => "ALQUIER, P. et GERBER, M. (2024). Universal Robust Regression via Maximum Mean Discrepancy. <i>Biometrika</i>, 111(1), pp. 71-92. ALQUIER, P. et GERBER, M. (2024). Universal Robust Regression via Maximum Mean Discrepancy. <i>Biome "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "GERBER Mathieu"
]
]
"ouvrage" => ""
"keywords" => array:3 [
0 => "Maximum mean discrepancy"
1 => "Minimum distance estimator"
2 => "Robust regression"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1093/biomet/asad031"
"publicationInfo" => array:3 [
"pages" => "71-92"
"volume" => "111"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Many modern datasets are collected automatically and are thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models, or generalized linear models, and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on maximum mean discrepancy minimization. We build two estimators which are both proven to be robust to Huber-type contamination. We obtain a non-asymptotic error bound for them and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators we derive new results on kernel conditional mean embedding of distributions which are of independent interest. Many modern datasets are collected automatically and are thus easily contaminated by outliers. This "
"en" => "Many modern datasets are collected automatically and are thus easily contaminated by outliers. This has led to a renewed interest in robust estimation, including new notions of robustness such as robustness to adversarial contamination of the data. However, most robust estimation methods are designed for a specific model. Notably, many methods were proposed recently to obtain robust estimators in linear models, or generalized linear models, and a few were developed for very specific settings, for example beta regression or sample selection models. In this paper we develop a new approach for robust estimation in arbitrary regression models, based on maximum mean discrepancy minimization. We build two estimators which are both proven to be robust to Huber-type contamination. We obtain a non-asymptotic error bound for them and show that it is also robust to adversarial contamination, but this estimator is computationally more expensive to use in practice than the other one. As a by-product of our theoretical analysis of the proposed estimators we derive new results on kernel conditional mean embedding of distributions which are of independent interest. Many modern datasets are collected automatically and are thus easily contaminated by outliers. This "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
68 => Essec\Faculty\Model\Contribution {#2340
#_index: "academ_contributions"
#_id: "14098"
#_source: array:18 [
"id" => "14098"
"slug" => "14098-pac-bayesian-offline-contextual-bandits-with-guarantees"
"yearMonth" => "2023-07"
"year" => "2023"
"title" => "PAC-Bayesian Offline Contextual Bandits With Guarantees"
"description" => "SAKHI, O., ALQUIER, P. et CHOPIN, N. (2023). PAC-Bayesian Offline Contextual Bandits With Guarantees. Dans: <i>40th International Conference on Machine Learning (ICML)</i>. Hawaii: Proceedings of Machine Learning Research, pp. 29777-29799. SAKHI, O., ALQUIER, P. et CHOPIN, N. (2023). PAC-Bayesian Offline Contextual Bandits With Guarantees "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "SAKHI Otmane"
]
2 => array:1 [
"name" => "CHOPIN Nicolas"
]
]
"ouvrage" => "40th International Conference on Machine Learning (ICML)"
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://proceedings.mlr.press/v202/sakhi23a.html"
"publicationInfo" => array:3 [
"pages" => "29777-29799"
"volume" => "202"
"number" => null
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "Royaume-Uni"
"en" => "United Kingdom"
]
"abstract" => array:2 [
"fr" => null
"en" => null
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
69 => Essec\Faculty\Model\Contribution {#2341
#_index: "academ_contributions"
#_id: "14619"
#_source: array:18 [
"id" => "14619"
"slug" => "14619-robust-estimation-and-regression-with-mmd"
"yearMonth" => "2024-01"
"year" => "2024"
"title" => "Robust estimation and regression with MMD"
"description" => "ALQUIER, P. et GERBER, M. (2024). Robust estimation and regression with MMD. Dans: The Mathematics of Data: Workshop on Optimization and Discrete Structures. Singapore. ALQUIER, P. et GERBER, M. (2024). Robust estimation and regression with MMD. Dans: The Mathematics o "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "GERBER Mathieu"
]
]
"ouvrage" => "The Mathematics of Data: Workshop on Optimization and Discrete Structures"
"keywords" => array:2 [
0 => "Maximum Mean Discrepancy"
1 => "robustness"
]
"updatedAt" => "2024-01-04 11:15:43"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Invité dans une conférence académique (Keynote speaker)"
"en" => "Invited speaker at an academic conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Maximum Mean Discrepancy (MMD, based on suitable kernels) leads to estimation procedures that are consistent without any assumption on the model nor on the data-generating process. This leads to strong robustness properties in practice, and this method was already used in complex models with promising results: estimation of SDE coefficients, ccopulas, data compression, generative models in AI. Maximum Mean Discrepancy (MMD, based on suitable kernels) leads to estimation procedures that are co "
"en" => "Maximum Mean Discrepancy (MMD, based on suitable kernels) leads to estimation procedures that are consistent without any assumption on the model nor on the data-generating process. This leads to strong robustness properties in practice, and this method was already used in complex models with promising results: estimation of SDE coefficients, ccopulas, data compression, generative models in AI. Maximum Mean Discrepancy (MMD, based on suitable kernels) leads to estimation procedures that are co "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
70 => Essec\Faculty\Model\Contribution {#2342
#_index: "academ_contributions"
#_id: "14643"
#_source: array:18 [
"id" => "14643"
"slug" => "14643-user-friendly-introduction-to-pac-bayes-bounds"
"yearMonth" => "2024-01"
"year" => "2024"
"title" => "User-friendly Introduction to PAC-Bayes Bounds"
"description" => "ALQUIER, P. (2024). <i>User-friendly Introduction to PAC-Bayes Bounds</i>. Boston - Delft: now publishers. ALQUIER, P. (2024). <i>User-friendly Introduction to PAC-Bayes Bounds</i>. Boston - Delft: now publi "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:9 [
0 => "Deep learning"
1 => "Model choice"
2 => "Online learning"
3 => "Variational inference"
4 => "Bayesian learning"
5 => "Classification and prediction"
6 => "Statistical learning theory"
7 => "Learning and statistical methods"
8 => "Information theory and statistics"
]
"updatedAt" => "2024-05-27 17:51:39"
"publicationUrl" => "https://www.nowpublishers.com/article/Details/MAL-100"
"publicationInfo" => array:3 [
"pages" => ""
"volume" => "17(2)"
"number" => ""
]
"type" => array:2 [
"fr" => "Livres"
"en" => "Books"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => """
Probably almost correct (PAC) bounds have been an intensive field of research over the last two decades. Hundreds of papers have been published and much progress has been made resulting in PAC-Bayes bounds becoming an important technique in machine learning.\n Probably almost correct (PAC) bounds have been an intensive field of research over the last two deca
The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial, the author guides the reader through the topic’s complexity and large body of publications. Covering both empirical and oracle PAC-bounds, this book serves as a primer for students and researchers who want to get to grips quickly with the subject. It provides a friendly introduction that illuminates the basic theory and points to the most important publications to gain deeper understanding of any particular aspect. The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial,
"""
"en" => """
Probably almost correct (PAC) bounds have been an intensive field of research over the last two decades. Hundreds of papers have been published and much progress has been made resulting in PAC-Bayes bounds becoming an important technique in machine learning.\n Probably almost correct (PAC) bounds have been an intensive field of research over the last two deca
\n
The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial, the author guides the reader through the topic’s complexity and large body of publications. Covering both empirical and oracle PAC-bounds, this book serves as a primer for students and researchers who want to get to grips quickly with the subject. It provides a friendly introduction that illuminates the basic theory and points to the most important publications to gain deeper understanding of any particular aspect. The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial,
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
71 => Essec\Faculty\Model\Contribution {#2343
#_index: "academ_contributions"
#_id: "14700"
#_source: array:18 [
"id" => "14700"
"slug" => "14700-dimension-free-bounds-for-sums-of-dependend-matrices-and-operators-with-heavy-tailed-distribution 14700-dimension-free-bounds-for-sums-of-dependend-matrices-and-operators-with-heavy-tailed-distribut "
"yearMonth" => "2024-02"
"year" => "2024"
"title" => "Dimension-free bounds for sums of dependend matrices and operators with heavy-tailed distribution"
"description" => "NAKAKITA, S., ALQUIER, P. et IMAIZUMI, M. (2024). Dimension-free bounds for sums of dependend matrices and operators with heavy-tailed distribution. <i>The Electronic Journal of Statistics</i>, 18(1), pp. 1130-1159. NAKAKITA, S., ALQUIER, P. et IMAIZUMI, M. (2024). Dimension-free bounds for sums of dependend matric "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "NAKAKITA Shogo"
]
2 => array:1 [
"name" => "IMAIZUMI Masaaki"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "Dependent process"
1 => "heavy-tailed distribution"
2 => "high-dimension"
3 => "random matrix"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/24-EJS2224"
"publicationInfo" => array:3 [
"pages" => "1130-1159"
"volume" => "18"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We study the deviation inequality for a sum of high-dimensional random matrices and operators with dependence and arbitrary heavy tails. There is an increase in the importance of the problem of estimating high-dimensional matrices, and dependence and heavy-tail properties of data are among the most critical topics currently. In this paper, we derive a dimension-free upper bound on the deviation, that is, the bound does not depend explicitly on the dimension of matrices, but depends on their effective rank. Our result is a generalization of several existing studies on the deviation of the sum of matrices. Our proof is based on two techniques: (i) a variational approximation of the dual of moment generating functions, and (ii) robustification through truncation of eigenvalues of matrices. We show that our results are applicable to several problems such as covariance matrix estimation, hidden Markov models, and overparameterized linear regression models. We study the deviation inequality for a sum of high-dimensional random matrices and operators with d "
"en" => "We study the deviation inequality for a sum of high-dimensional random matrices and operators with dependence and arbitrary heavy tails. There is an increase in the importance of the problem of estimating high-dimensional matrices, and dependence and heavy-tail properties of data are among the most critical topics currently. In this paper, we derive a dimension-free upper bound on the deviation, that is, the bound does not depend explicitly on the dimension of matrices, but depends on their effective rank. Our result is a generalization of several existing studies on the deviation of the sum of matrices. Our proof is based on two techniques: (i) a variational approximation of the dual of moment generating functions, and (ii) robustification through truncation of eigenvalues of matrices. We show that our results are applicable to several problems such as covariance matrix estimation, hidden Markov models, and overparameterized linear regression models. We study the deviation inequality for a sum of high-dimensional random matrices and operators with d "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
72 => Essec\Faculty\Model\Contribution {#2344
#_index: "academ_contributions"
#_id: "14731"
#_source: array:18 [
"id" => "14731"
"slug" => "14731-introduction-to-pac-bayes-bounds"
"yearMonth" => "2024-03"
"year" => "2024"
"title" => "Introduction to PAC-Bayes bounds"
"description" => "ALQUIER, P. (2024). Introduction to PAC-Bayes bounds. Dans: Machine Learning Summer School in Okinawa 2024. Okinawa. ALQUIER, P. (2024). Introduction to PAC-Bayes bounds. Dans: Machine Learning Summer School in Okinaw "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "Machine Learning Summer School in Okinawa 2024"
"keywords" => array:9 [
0 => "Deep learning"
1 => "Model choice"
2 => "Online learning"
3 => "Variational inference"
4 => "Bayesian learning"
5 => "Classification and prediction"
6 => "Statistical learning theory"
7 => "Learning and statistical methods"
8 => "Information theory and statistics"
]
"updatedAt" => "2024-03-06 17:38:38"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Invité dans une conférence académique (Keynote speaker)"
"en" => "Invited speaker at an academic conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => """
Probably approximately correct (PAC) bounds have been an intensive field of research over the last two decades. Hundreds of papers have been published and much progress has been made resulting in PAC-Bayes bounds becoming an important technique in machine learning.\n Probably approximately correct (PAC) bounds have been an intensive field of research over the last t
\n
The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial, the author guides the reader through the topic’s complexity and large body of publications. Covering both empirical and oracle PAC-bounds, this book serves as a primer for students and researchers who want to get to grips quickly with the subject. It provides a friendly introduction that illuminates the basic theory and points to the most important publications to gain deeper understanding of any particular aspect. The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial,
"""
"en" => """
Probably approximately correct (PAC) bounds have been an intensive field of research over the last two decades. Hundreds of papers have been published and much progress has been made resulting in PAC-Bayes bounds becoming an important technique in machine learning.\n Probably approximately correct (PAC) bounds have been an intensive field of research over the last t
\n
The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial, the author guides the reader through the topic’s complexity and large body of publications. Covering both empirical and oracle PAC-bounds, this book serves as a primer for students and researchers who want to get to grips quickly with the subject. It provides a friendly introduction that illuminates the basic theory and points to the most important publications to gain deeper understanding of any particular aspect. The proliferation of research has made the field for a newcomer somewhat daunting. In this tutorial,
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
73 => Essec\Faculty\Model\Contribution {#2345
#_index: "academ_contributions"
#_id: "14737"
#_source: array:18 [
"id" => "14737"
"slug" => "14737-optimistic-estimation-of-convergence-in-markov-chains-with-the-average-mixing-time"
"yearMonth" => "2024-07"
"year" => "2024"
"title" => "Optimistic Estimation of Convergence in Markov Chains with the Average Mixing Time"
"description" => "WOLFER, G. et ALQUIER, P. (2024). Optimistic Estimation of Convergence in Markov Chains with the Average Mixing Time. Dans: International Conference on Scientific Computation and Differential Equations. Singapore. WOLFER, G. et ALQUIER, P. (2024). Optimistic Estimation of Convergence in Markov Chains with the Ave "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "WOLFER Geoffrey"
]
]
"ouvrage" => "International Conference on Scientific Computation and Differential Equations"
"keywords" => array:1 [
0 => "Markov chains"
]
"updatedAt" => "2024-07-15 12:32:43"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Communications dans une conférence"
"en" => "Presentations at an Academic or Professional conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications. The convergence rate of a Markov chain to its stationary distribution is typically assessed using th "
"en" => "The convergence rate of a Markov chain to its stationary distribution is typically assessed using the concept of total variation mixing time. However, this worst-case measure often yields pessimistic estimates and is challenging to infer from observations. In this paper, we advocate for the use of the average-mixing time as a more optimistic and demonstrably easier-to-estimate alternative. We further illustrate its applicability across a range of settings, from two-point to countable spaces, and discuss some practical implications. The convergence rate of a Markov chain to its stationary distribution is typically assessed using th "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
74 => Essec\Faculty\Model\Contribution {#2346
#_index: "academ_contributions"
#_id: "14738"
#_source: array:18 [
"id" => "14738"
"slug" => "14738-pac-bayesian-offline-contextual-bandits-with-guarantees"
"yearMonth" => "2024-07"
"year" => "2024"
"title" => "PAC-Bayesian Offline Contextual Bandits With Guarantees"
"description" => "SAKHI, O., ALQUIER, P. et CHOPIN, N. (2024). PAC-Bayesian Offline Contextual Bandits With Guarantees. Dans: Closing Workshop of the ISBA Programme on Interpretable Inference via Principled BNP Approaches in Biomedical Research and Beyond. Singapore. SAKHI, O., ALQUIER, P. et CHOPIN, N. (2024). PAC-Bayesian Offline Contextual Bandits With Guarantees "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "SAKHI Otmane"
]
2 => array:1 [
"name" => "CHOPIN Nicolas"
]
]
"ouvrage" => "Closing Workshop of the ISBA Programme on Interpretable Inference via Principled BNP Approaches in Biomedical Research and Beyond Closing Workshop of the ISBA Programme on Interpretable Inference via Principled BNP Approaches in B "
"keywords" => []
"updatedAt" => "2024-07-31 12:31:43"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Invité dans une conférence académique (Keynote speaker)"
"en" => "Invited speaker at an academic conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => "This work introduces a new principled approach for off-policy learning in contextual bandits. Unlike previous work, our approach does not derive learning principles from intractable or loose bounds. We analyse the problem through the PAC-Bayesian lens, interpreting policies as mixtures of decision rules. This allows us to propose novel generalization bounds and provide tractable algorithms to optimize them. We prove that the derived bounds are tighter than their competitors, and can be optimized directly to confidently improve upon the logging policy offline. Our approach learns policies with guarantees, uses all available data and does not require tuning additional hyperparameters on held-out sets. We demonstrate through extensive experiments the effectiveness of our approach in providing performance guarantees in practical scenarios. This work introduces a new principled approach for off-policy learning in contextual bandits. Unlike "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
75 => Essec\Faculty\Model\Contribution {#2347
#_index: "academ_contributions"
#_id: "14795"
#_source: array:18 [
"id" => "14795"
"slug" => "14795-deepfakes-a-comms-persons-friend-or-foe"
"yearMonth" => "2024-05"
"year" => "2024"
"title" => "Deepfakes: a comms person's friend or foe?"
"description" => "ALQUIER, P. 2024. <i>Deepfakes: a comms person's friend or foe?</i> Mai."
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "Deepfakes"
1 => "AI"
2 => "corporate communication"
3 => "public relations"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://www.mynewsdesk.com/sg/hong-bao-media/videos/119588"
"publicationInfo" => array:3 [
"pages" => null
"volume" => null
"number" => null
]
"type" => array:2 [
"fr" => "Interviews : Emission radio - TV - presse écrite"
"en" => "Interviews: radio - TV - press"
]
"support_type" => array:2 [
"fr" => "Presse"
"en" => "Press"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => """
There is a dark side to the exciting Generative AI trend: deepfakes. But whether deepfakes are used for good or for ill is still up to the person creating them. So, what scope is there for communications professionals to use deepfakes? Appropriately? What would constitute an inappropriate use? Join us to hear from our expert speakers.\n There is a dark side to the exciting Generative AI trend: deepfakes. But whether deepfakes are used
In this discussion, Mark Laudi and Pierre Alquier lay bare how easy it is to create a deepfake and what the limitations are, and they give participants the chance to create one using a video of themselves. They also share how to detect them. In this discussion, Mark Laudi and Pierre Alquier lay bare how easy it is to create a deepfake and w
"""
"en" => """
There is a dark side to the exciting Generative AI trend: deepfakes. But whether deepfakes are used for good or for ill is still up to the person creating them. So, what scope is there for communications professionals to use deepfakes? Appropriately? What would constitute an inappropriate use? Join us to hear from our expert speakers.\n There is a dark side to the exciting Generative AI trend: deepfakes. But whether deepfakes are used
In this discussion, Mark Laudi and Pierre Alquier lay bare how easy it is to create a deepfake and what the limitations are, and they give participants the chance to create one using a video of themselves. They also share how to detect them. In this discussion, Mark Laudi and Pierre Alquier lay bare how easy it is to create a deepfake and w
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
76 => Essec\Faculty\Model\Contribution {#2348
#_index: "academ_contributions"
#_id: "14839"
#_source: array:18 [
"id" => "14839"
"slug" => "14839-pac-bayesian-bounds-with-applications-to-deep-learning-and-offline-contextual-bandits"
"yearMonth" => "2024-08"
"year" => "2024"
"title" => "PAC-Bayesian Bounds, with applications to Deep Learning and Offline Contextual Bandits"
"description" => "ALQUIER, P. (2024). PAC-Bayesian Bounds, with applications to Deep Learning and Offline Contextual Bandits. Dans: International Conference on Mathematical Theory of Deep Learning, Chinese Academy of Science. Beijing. ALQUIER, P. (2024). PAC-Bayesian Bounds, with applications to Deep Learning and Offline Contextual B "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "International Conference on Mathematical Theory of Deep Learning, Chinese Academy of Science"
"keywords" => []
"updatedAt" => "2024-08-26 16:23:11"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Invité dans une conférence académique (Keynote speaker)"
"en" => "Invited speaker at an academic conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
77 => Essec\Faculty\Model\Contribution {#2349
#_index: "academ_contributions"
#_id: "14980"
#_source: array:18 [
"id" => "14980"
"slug" => "14980-pac-bayes-bounds-understanding-the-generalization-of-bayesian-learning-algorithms"
"yearMonth" => "2024-10"
"year" => "2024"
"title" => "PAC-Bayes bounds: understanding the generalization of Bayesian learning algorithms."
"description" => "ALQUIER, P. (2024). PAC-Bayes bounds: understanding the generalization of Bayesian learning algorithms. Dans: Stochastics Seminar, Department of Mathematics, NUS. Singapore. ALQUIER, P. (2024). PAC-Bayes bounds: understanding the generalization of Bayesian learning algorith "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "Stochastics Seminar, Department of Mathematics, NUS"
"keywords" => array:1 [
0 => "Machine learning, neural networks, information theory."
]
"updatedAt" => "2024-10-14 10:15:49"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Présentations dans un séminaire de recherche"
"en" => "Presentations at a Faculty research seminar"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => ""
"en" => """
The PAC-Bayesian theory provides tools to understand the accuracy of Bayes-inspired algorithms that learn probability distributions on parameters. This theory was initially developed by McAllester about 20 years ago, and applied successfully\n The PAC-Bayesian theory provides tools to understand the accuracy of Bayes-inspired algorithms that
to various machine learning algorithms in various problems. Recently, it led to tight generalization bounds for deep neural networks, a task that could not be achieved by standard "worst-case" generalization bounds such as Vapnik-Chervonenkis bounds. In this talk, I will provide a brief introduction to PAC-Bayes bounds, and explain the core ideas of the theory. I will also provide an overview of the recent research directions. In particular, I will highlight the application of PAC-Bayes bounds to derive minimax-optimal rates of convergence in classification and in regression, and the connection to mutual-information bounds. to various machine learning algorithms in various problems. Recently, it led to tight generalization
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
78 => Essec\Faculty\Model\Contribution {#2350
#_index: "academ_contributions"
#_id: "15017"
#_source: array:18 [
"id" => "15017"
"slug" => "15017-2-lectures-on-pac-bayes-bounds"
"yearMonth" => "2025-01"
"year" => "2025"
"title" => "2 lectures on PAC-Bayes bounds"
"description" => "ALQUIER, P. (2025). 2 lectures on PAC-Bayes bounds. Dans: Heidelberg-Paris Workshop on Mathematical Statistics. Heidelberg. ALQUIER, P. (2025). 2 lectures on PAC-Bayes bounds. Dans: Heidelberg-Paris Workshop on Mathematical "
"authors" => array:1 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
]
"ouvrage" => "Heidelberg-Paris Workshop on Mathematical Statistics"
"keywords" => array:3 [
0 => "PAC-Bayesian theory"
1 => "Bayes-inspired algorithms"
2 => "Machine learning algorithms"
]
"updatedAt" => "2025-03-03 10:28:39"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Invité dans une conférence académique (Keynote speaker)"
"en" => "Invited speaker at an academic conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "The PAC-Bayesian theory provides tools to understand the accuracy of Bayes-inspired algorithms that learn probability distributions on parameters. This theory was initially developed by McAllester about 20 years ago, and applied successfully to various machine learning algorithms in various problems. Recently, it led to tight generalization bounds for deep neural networks, a task that could not be achieved by standard "worst-case" generalization bounds such as Vapnik-Chervonenkis bounds. In a first part, I will provide a brief introduction to PAC-Bayes bounds, explain the core ideas and the main applications. I will also provide an overview of the recent research trends. In a second time, I will discuss more theoretical aspects. In particular, I will highlight the application of PAC-Bayes bounds to derive minimax-optimal rates of convergence in classification and in regression, and the connection to mutual-information bounds. The PAC-Bayesian theory provides tools to understand the accuracy of Bayes-inspired algorithms that "
"en" => "The PAC-Bayesian theory provides tools to understand the accuracy of Bayes-inspired algorithms that learn probability distributions on parameters. This theory was initially developed by McAllester about 20 years ago, and applied successfully to various machine learning algorithms in various problems. Recently, it led to tight generalization bounds for deep neural networks, a task that could not be achieved by standard "worst-case" generalization bounds such as Vapnik-Chervonenkis bounds. In a first part, I will provide a brief introduction to PAC-Bayes bounds, explain the core ideas and the main applications. I will also provide an overview of the recent research trends. In a second time, I will discuss more theoretical aspects. In particular, I will highlight the application of PAC-Bayes bounds to derive minimax-optimal rates of convergence in classification and in regression, and the connection to mutual-information bounds. The PAC-Bayesian theory provides tools to understand the accuracy of Bayes-inspired algorithms that "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
79 => Essec\Faculty\Model\Contribution {#2351
#_index: "academ_contributions"
#_id: "15029"
#_source: array:18 [
"id" => "15029"
"slug" => "15029-convergence-of-statistical-estimators-via-mutual-information-bounds"
"yearMonth" => "2025-03"
"year" => "2025"
"title" => "Convergence of Statistical Estimators via Mutual Information Bounds"
"description" => "ALQUIER, P. et KHRIBCH, E.M. (2025). Convergence of Statistical Estimators via Mutual Information Bounds. Dans: Okinawa Institute of Science and Technology Machine Learning Workshop. Okinawa. ALQUIER, P. et KHRIBCH, E.M. (2025). Convergence of Statistical Estimators via Mutual Information Bo "
"authors" => array:2 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "KHRIBCH EL Mahdi"
]
]
"ouvrage" => "Okinawa Institute of Science and Technology Machine Learning Workshop"
"keywords" => []
"updatedAt" => "2025-03-04 10:37:01"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Invité dans une conférence académique (Keynote speaker)"
"en" => "Invited speaker at an academic conference"
]
"support_type" => array:2 [
"fr" => null
"en" => null
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for statistical models. The derived bound has wide-ranging applications in statistical inference. It yields improved contraction rates for fractional posteriors in Bayesian nonparametrics. It can also be used to study a wide range of estimation methods, such as variational inference or Maximum Likelihood Estimation (MLE). By bridging these diverse areas, this work advances our understanding of the fundamental limits of statistical inference and the role of information in learning from data. We hope that these results will not only clarify connections between statistical inference and information theory but also help to develop a new toolbox to study a wide range of estimators. Recent advances in statistical learning theory have revealed profound connections between mutual inf "
"en" => "Recent advances in statistical learning theory have revealed profound connections between mutual information (MI) bounds, PAC-Bayesian theory, and Bayesian nonparametrics. This work introduces a novel mutual information bound for statistical models. The derived bound has wide-ranging applications in statistical inference. It yields improved contraction rates for fractional posteriors in Bayesian nonparametrics. It can also be used to study a wide range of estimation methods, such as variational inference or Maximum Likelihood Estimation (MLE). By bridging these diverse areas, this work advances our understanding of the fundamental limits of statistical inference and the role of information in learning from data. We hope that these results will not only clarify connections between statistical inference and information theory but also help to develop a new toolbox to study a wide range of estimators. Recent advances in statistical learning theory have revealed profound connections between mutual inf "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
80 => Essec\Faculty\Model\Contribution {#2352
#_index: "academ_contributions"
#_id: "15169"
#_source: array:18 [
"id" => "15169"
"slug" => "15169-concentration-of-discrepancy-based-approximate-bayesian-computation-via-rademacher-complexity"
"yearMonth" => "2025-02"
"year" => "2025"
"title" => "Concentration of discrepancy-based approximate Bayesian computation via Rademacher complexity"
"description" => "LEGRAMANTI, S., DURANTE, D. et ALQUIER, P. (2025). Concentration of discrepancy-based approximate Bayesian computation via Rademacher complexity. <i>Annals of Statistics</i>, 53(1), pp. 37-60. LEGRAMANTI, S., DURANTE, D. et ALQUIER, P. (2025). Concentration of discrepancy-based approximate Ba "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "LEGRAMANTI Sirio"
]
2 => array:1 [
"name" => "DURANTE Daniele"
]
]
"ouvrage" => ""
"keywords" => array:5 [
0 => "Approximate Bayesian computation"
1 => "Integral probability semimetrics"
2 => "Maximum mean discrepancy"
3 => "Rademacher complexity"
4 => "Wasserstein distance"
]
"updatedAt" => "2025-03-10 16:55:02"
"publicationUrl" => "https://doi.org/10.1214/24-AOS2453"
"publicationInfo" => array:3 [
"pages" => "37-60"
"volume" => "53"
"number" => "1"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "There has been an increasing interest on summary-free versions of approximate Bayesian computation (ABC), which replace distances among summaries with discrepancies between the empirical distributions of the observed data and the synthetic samples generated under the proposed parameter values. The success of these solutions has motivated theoretical studies on the limiting properties of the induced posteriors. However, current results (i) are often tailored to a specific discrepancy, (ii) require, either explicitly or implicitly, regularity conditions on the data generating process and the assumed statistical model, and (iii) yield bounds depending on sequences of control functions that are not made explicit. As such, there is the lack of a theoretical framework that (i) is unified, (ii) facilitates the derivation of limiting properties that hold uniformly, and (iii) relies on verifiable assumptions that provide concentration bounds clarifying which factors govern the limiting behavior of the ABC posterior. We address this gap via a novel theoretical framework that introduces the concept of Rademacher complexity in the analysis of the limiting properties for discrepancy-based ABC posteriors. This yields a unified theory that relies on constructive arguments and provides more informative asymptotic results and uniform concentration bounds, even in settings not covered by current studies. These advancements are obtained by relating the properties of summary-free ABC posteriors to the behavior of the Rademacher complexity associated with the chosen discrepancy within the family of integral probability semimetrics. This family extends summary-based ABC, and includes the Wasserstein distance and maximum mean discrepancy (MMD), among others. As clarified through a focus on the MMD case and via illustrative simulations, this perspective yields an improved understanding of summary-free ABC. There has been an increasing interest on summary-free versions of approximate Bayesian computation ( "
"en" => "There has been an increasing interest on summary-free versions of approximate Bayesian computation (ABC), which replace distances among summaries with discrepancies between the empirical distributions of the observed data and the synthetic samples generated under the proposed parameter values. The success of these solutions has motivated theoretical studies on the limiting properties of the induced posteriors. However, current results (i) are often tailored to a specific discrepancy, (ii) require, either explicitly or implicitly, regularity conditions on the data generating process and the assumed statistical model, and (iii) yield bounds depending on sequences of control functions that are not made explicit. As such, there is the lack of a theoretical framework that (i) is unified, (ii) facilitates the derivation of limiting properties that hold uniformly, and (iii) relies on verifiable assumptions that provide concentration bounds clarifying which factors govern the limiting behavior of the ABC posterior. We address this gap via a novel theoretical framework that introduces the concept of Rademacher complexity in the analysis of the limiting properties for discrepancy-based ABC posteriors. This yields a unified theory that relies on constructive arguments and provides more informative asymptotic results and uniform concentration bounds, even in settings not covered by current studies. These advancements are obtained by relating the properties of summary-free ABC posteriors to the behavior of the Rademacher complexity associated with the chosen discrepancy within the family of integral probability semimetrics. This family extends summary-based ABC, and includes the Wasserstein distance and maximum mean discrepancy (MMD), among others. As clarified through a focus on the MMD case and via illustrative simulations, this perspective yields an improved understanding of summary-free ABC. There has been an increasing interest on summary-free versions of approximate Bayesian computation ( "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
81 => Essec\Faculty\Model\Contribution {#2353
#_index: "academ_contributions"
#_id: "15212"
#_source: array:18 [
"id" => "15212"
"slug" => "15212-logarithmic-smoothing-for-pessimistic-off-policy-evaluation-selection-and-learning"
"yearMonth" => "2024-12"
"year" => "2024"
"title" => "Logarithmic Smoothing for Pessimistic Off-Policy Evaluation, Selection and Learning"
"description" => "SAKHI, O., AOUALI, I., ALQUIER, P. et CHOPIN, N. (2024). Logarithmic Smoothing for Pessimistic Off-Policy Evaluation, Selection and Learning. Dans: <i>38th Conference on Neural Information Processing Systems (NeurIPS'24)</i>. Vancouver: Curran Associates, Inc, pp. 80706-80755. SAKHI, O., AOUALI, I., ALQUIER, P. et CHOPIN, N. (2024). Logarithmic Smoothing for Pessimistic Off-P "
"authors" => array:4 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "SAKHI Otmane"
]
2 => array:1 [
"name" => "AOUALI Imad"
]
3 => array:1 [
"name" => "CHOPIN Nicolas"
]
]
"ouvrage" => "38th Conference on Neural Information Processing Systems (NeurIPS'24)"
"keywords" => []
"updatedAt" => "2025-04-02 09:13:33"
"publicationUrl" => "https://arxiv.org/abs/2405.14335"
"publicationInfo" => array:3 [
"pages" => "80706-80755"
"volume" => ""
"number" => ""
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
]
"support_type" => array:2 [
"fr" => "Editeur"
"en" => "Publisher"
]
"countries" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
"abstract" => array:2 [
"fr" => "This work investigates the offline formulation of the contextual bandit problem, where the goal is to leverage past interactions collected under a behavior policy to evaluate, select, and learn new, potentially better-performing, policies. Motivated by critical applications, we move beyond point estimators. Instead, we adopt the principle of pessimism where we construct upper bounds that assess a policy's worst-case performance, enabling us to confidently select and learn improved policies. Precisely, we introduce novel, fully empirical concentration bounds for a broad class of importance weighting risk estimators. These bounds are general enough to cover most existing estimators and pave the way for the development of new ones. In particular, our pursuit of the tightest bound within this class motivates a novel estimator (LS), that logarithmically smooths large importance weights. The bound for LS is provably tighter than all its competitors, and naturally results in improved policy selection and learning strategies. Extensive policy evaluation, selection, and learning experiments highlight the versatility and favorable performance of LS. This work investigates the offline formulation of the contextual bandit problem, where the goal is t "
"en" => "This work investigates the offline formulation of the contextual bandit problem, where the goal is to leverage past interactions collected under a behavior policy to evaluate, select, and learn new, potentially better-performing, policies. Motivated by critical applications, we move beyond point estimators. Instead, we adopt the principle of pessimism where we construct upper bounds that assess a policy's worst-case performance, enabling us to confidently select and learn improved policies. Precisely, we introduce novel, fully empirical concentration bounds for a broad class of importance weighting risk estimators. These bounds are general enough to cover most existing estimators and pave the way for the development of new ones. In particular, our pursuit of the tightest bound within this class motivates a novel estimator (LS), that logarithmically smooths large importance weights. The bound for LS is provably tighter than all its competitors, and naturally results in improved policy selection and learning strategies. Extensive policy evaluation, selection, and learning experiments highlight the versatility and favorable performance of LS. This work investigates the offline formulation of the contextual bandit problem, where the goal is t "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
82 => Essec\Faculty\Model\Contribution {#2354
#_index: "academ_contributions"
#_id: "15424"
#_source: array:18 [
"id" => "15424"
"slug" => "15424-bayes-meets-bernstein-at-the-meta-level-an-analysis-of-fast-rates-in-meta-learning-with-pac-bayes 15424-bayes-meets-bernstein-at-the-meta-level-an-analysis-of-fast-rates-in-meta-learning-with-pac-ba "
"yearMonth" => "2025-02"
"year" => "2025"
"title" => "Bayes Meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayes"
"description" => "RIOU, C., ALQUIER, P. et CHÉRIEF-ABDELLATIF, B.E. (2025). Bayes Meets Bernstein at the Meta Level: an Analysis of Fast Rates in Meta-Learning with PAC-Bayes. <i>Journal of Machine Learning Research</i>, 26(2), pp. 1-60. RIOU, C., ALQUIER, P. et CHÉRIEF-ABDELLATIF, B.E. (2025). Bayes Meets Bernstein at the Meta Level: a "
"authors" => array:3 [
0 => array:3 [
"name" => "ALQUIER Pierre"
"bid" => "B00809923"
"slug" => "alquier-pierre"
]
1 => array:1 [
"name" => "RIOU Charles"
]
2 => array:1 [
"name" => "CHÉRIEF-ABDELLATIF Badr-Eddine"
]
]
"ouvrage" => ""
"keywords" => array:7 [
0 => "Bernstein’s condition"
1 => "meta-learning"
2 => "fast rates"
3 => "PAC-Bayes bounds"
4 => "information bounds"
5 => "the Gibbs algorithm"
6 => "variational approximations."
]
"updatedAt" => "2025-02-14 01:00:42"
"publicationUrl" => "https://jmlr.org/papers/v26/23-025.html"
"publicationInfo" => array:3 [
"pages" => "1-60"
"volume" => "26"
"number" => "2"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
]
"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
"abstract" => array:2 [
"fr" => "Bernstein’s condition is a key assumption that guarantees fast rates in machine learning. For example, under this condition, the Gibbs posterior with prior π has an excess risk in O(√(d/n)), as opposed to O(d/n) in the general case, where n denotes the number of observations and d is a complexity parameter which depends on the prior π. In this paper, we examine the Gibbs posterior in the context of meta-learning, i.e., when learning the prior π from T previous tasks. Our main result is that Bernstein’s condition always holds at the meta level, regardless of its validity at the observation level. This implies that the additional cost to learn the Gibbs prior π, which will reduce the term d across tasks, is in O(1/T), instead of the expected O(1/√T). We further illustrate how this result improves on the standard rates in three different settings: discrete priors, Gaussian priors and mixture of Gaussian priors. Bernstein’s condition is a key assumption that guarantees fast rates in machine learning. For exampl "
"en" => "Bernstein’s condition is a key assumption that guarantees fast rates in machine learning. For example, under this condition, the Gibbs posterior with prior π has an excess risk in O(√(d/n)), as opposed to O(d/n) in the general case, where n denotes the number of observations and d is a complexity parameter which depends on the prior π. In this paper, we examine the Gibbs posterior in the context of meta-learning, i.e., when learning the prior π from T previous tasks. Our main result is that Bernstein’s condition always holds at the meta level, regardless of its validity at the observation level. This implies that the additional cost to learn the Gibbs prior π, which will reduce the term d across tasks, is in O(1/T), instead of the expected O(1/√T). We further illustrate how this result improves on the standard rates in three different settings: discrete priors, Gaussian priors and mixture of Gaussian priors. Bernstein’s condition is a key assumption that guarantees fast rates in machine learning. For exampl "
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2025-04-02T19:21:40.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 4.6238337
+"parent": null
}
]
"avatar" => "https://faculty.essec.edu/wp-content/uploads/avatars/B00809923.jpg"
"contributionCounts" => 83
"personalLinks" => array:3 [
0 => "<a href="https://orcid.org/0000-0003-4249-7337" target="_blank">ORCID</a>"
1 => "<a href="https://scholar.google.com/citations?user=ngkCAJYAAAAJ" target="_blank">Google scholar</a>"
2 => "<a href="https://pierrealquier.github.io/" target="_blank">Personal site</a>"
]
"docTitle" => "Pierre ALQUIER"
"docSubtitle" => "Professor"
"docDescription" => "Department: Information Systems, Data Analytics and Operations<br>Campus de Singapour"
"docType" => "cv"
"docPreview" => "<img src="https://faculty.essec.edu/wp-content/uploads/avatars/B00809923.jpg"><span><span>Pierre ALQUIER</span><span>B00809923</span></span> <img src="https://faculty.essec.edu/wp-content/uploads/avatars/B00809923.jpg"><span><span>Pierre ALQ "
"academ_cv_info" => ""
]
#_index: "academ_cv"
+lang: "en"
+"_type": "_doc"
+"_score": 5.3343277
+"parent": null
}
