Essec\Faculty\Model\Profile {#2205
#_id: "B00791786"
#_source: array:39 [
"bid" => "B00791786"
"academId" => "27109"
"slug" => "ndaoud-mohamed"
"fullName" => "Mohamed NDAOUD"
"lastName" => "NDAOUD"
"firstName" => "Mohamed"
"title" => array:2 [
"fr" => "Professeur assistant"
"en" => "Assistant Professor"
]
"email" => "mohamed.ndaoud@essec.edu"
"status" => "ACTIF"
"campus" => "Campus de Cergy"
"departments" => []
"phone" => "0134433656"
"sites" => []
"facNumber" => "27109"
"externalCvUrl" => "https://faculty.essec.edu/cv/ndaoud-mohamed/pdf"
"googleScholarUrl" => "https://scholar.google.fr/citations?user=aZ2SLH8AAAAJ&hl=fr"
"facOrcId" => "https://orcid.org/0000-0002-0255-9815"
"career" => array:2 [
0 => Essec\Faculty\Model\CareerItem {#2211
#_index: null
#_id: null
#_source: array:7 [
"startDate" => "2021-06-01"
"endDate" => null
"isInternalPosition" => true
"type" => array:2 [
"fr" => "Positions académiques principales"
"en" => "Full-time academic appointments"
]
"label" => array:2 [
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"en" => "Assistant Professor"
]
"institution" => array:2 [
"fr" => "ESSEC Business School"
"en" => "ESSEC Business School"
]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
1 => Essec\Faculty\Model\CareerItem {#2212
#_index: null
#_id: null
#_source: array:7 [
"startDate" => "2021-06-01"
"endDate" => "2025-05-31"
"isInternalPosition" => true
"type" => array:2 [
"en" => "Other appointments"
"fr" => "Autres positions"
]
"label" => array:2 [
"fr" => "Responsable de chaire « Data Science »"
"en" => "Chaired Professor « Data Science »"
]
"institution" => array:2 [
"fr" => "ESSEC Business School"
"en" => "ESSEC Business School"
]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
]
"diplomes" => array:3 [
0 => Essec\Faculty\Model\Diplome {#2207
#_index: null
#_id: null
#_source: array:6 [
"diplome" => "DIPLOMA"
"type" => array:2 [
"fr" => "Diplômes"
"en" => "Diplomas"
]
"year" => "2019"
"label" => array:2 [
"en" => "Doctorate in Mathematical Statistics"
"fr" => "Doctorat en Statistiques Mathématiques"
]
"institution" => array:2 [
"fr" => "Université Paris-Saclay"
"en" => "Université Paris-Saclay"
]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
1 => Essec\Faculty\Model\Diplome {#2209
#_index: null
#_id: null
#_source: array:6 [
"diplome" => "DIPLOMA"
"type" => array:2 [
"fr" => "Diplômes"
"en" => "Diplomas"
]
"year" => "2016"
"label" => array:2 [
"en" => "Master of Science, Finance"
"fr" => "Master of Science, Finance"
]
"institution" => array:2 [
"fr" => "Université Pierre et Marie Curie (UPMC)"
"en" => "Université Pierre et Marie Curie (UPMC)"
]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
2 => Essec\Faculty\Model\Diplome {#2206
#_index: null
#_id: null
#_source: array:6 [
"diplome" => "DIPLOMA"
"type" => array:2 [
"fr" => "Diplômes"
"en" => "Diplomas"
]
"year" => "2015"
"label" => array:2 [
"en" => "Master of Engineering, Mathematics"
"fr" => "Ecole d'ingénieur, Mathématiques"
]
"institution" => array:2 [
"fr" => "École Polytechnique"
"en" => "École Polytechnique"
]
"country" => array:2 [
"fr" => "France"
"en" => "France"
]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
]
"bio" => array:2 [
"fr" => null
"en" => """
<p dir="ltr"><span style="color:rgb(33, 33, 33)">I have received a PhD in theoretical statistics, under the supervision of A.B. Tsybakov. Prior to that I graduated from Ecole Polytechnique majoring in applied mathematics.</span></p>\n
\n
<p dir="ltr">My research interests are in high dimensional probability and statistics. In particular, I have worked during my PhD on variable selection, estimation and community detection in the high dimensional setting. I am also interested in robust statistics, stochastic processes, harmonic analysis, random matrix theory and spiked models.</p>
"""
]
"department" => array:2 [
"fr" => "Systèmes d’information, sciences de la décision et statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"site" => array:2 [
"fr" => "https://sites.google.com/view/mndaoud/"
"en" => "https://www.linkedin.com/in/mohamed-ndaoud"
]
"industrrySectors" => array:2 [
"fr" => null
"en" => null
]
"researchFields" => array:2 [
"fr" => "Analyse des données statistiques - Sciences de la décision - Théorie des probabilités et statistiques"
"en" => "Statistical Data Analysis - Decision Sciences - Probability Theory & Mathematical Statistics"
]
"teachingFields" => array:2 [
"fr" => "Analyse des données statistiques - Théorie des probabilités et statistiques - Sciences de la décision - Mathématiques"
"en" => "Statistical Data Analysis - Probability Theory & Mathematical Statistics - Decision Sciences - Mathematics"
]
"distinctions" => array:3 [
0 => Essec\Faculty\Model\Distinction {#2213
#_index: null
#_id: null
#_source: array:6 [
"date" => "2020-01-01"
"label" => array:2 [
"fr" => "IMS New Researcher Travel Award"
"en" => "IMS New Researcher Travel Award"
]
"type" => array:2 [
"fr" => "Prix"
"en" => "Awards"
]
"tri" => " 1 "
"institution" => array:2 [
"fr" => null
"en" => null
]
"country" => array:2 [
"fr" => null
"en" => null
]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
1 => Essec\Faculty\Model\Distinction {#2214
#_index: null
#_id: null
#_source: array:6 [
"date" => "2020-01-01"
"label" => array:2 [
"fr" => "Zumberge Individual Award 2020"
"en" => "Zumberge Individual Award 2020"
]
"type" => array:2 [
"fr" => "Bourses"
"en" => "Grants"
]
"tri" => " 2 "
"institution" => array:2 [
"fr" => "University of South California (USC)"
"en" => "University of South California (USC)"
]
"country" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
2 => Essec\Faculty\Model\Distinction {#2215
#_index: null
#_id: null
#_source: array:6 [
"date" => "2019-01-01"
"label" => array:2 [
"fr" => "Best Student Paper Award"
"en" => "Best Student Paper Award"
]
"type" => array:2 [
"fr" => "Prix"
"en" => "Awards"
]
"tri" => " 1 "
"institution" => array:2 [
"fr" => null
"en" => null
]
"country" => array:2 [
"fr" => null
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]
]
+lang: "fr"
+"parent": Essec\Faculty\Model\Profile {#2205}
}
]
"teaching" => array:3 [
0 => Essec\Faculty\Model\TeachingItem {#2204
#_index: null
#_id: null
#_source: array:7 [
"startDate" => "2021"
"endDate" => "2021"
"program" => null
"label" => array:2 [
"fr" => "Analysis of Variance and Design"
"en" => "Analysis of Variance and Design"
]
"type" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"institution" => array:2 [
"fr" => "University of South California (USC)"
"en" => "University of South California (USC)"
]
"country" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
]
+lang: "fr"
}
1 => Essec\Faculty\Model\TeachingItem {#2210
#_index: null
#_id: null
#_source: array:7 [
"startDate" => "2020"
"endDate" => "2020"
"program" => null
"label" => array:2 [
"fr" => "Foundations of Statistical Learning Theory"
"en" => "Foundations of Statistical Learning Theory"
]
"type" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"institution" => array:2 [
"fr" => "University of South California (USC)"
"en" => "University of South California (USC)"
]
"country" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
]
+lang: "fr"
}
2 => Essec\Faculty\Model\TeachingItem {#2208
#_index: null
#_id: null
#_source: array:7 [
"startDate" => "2019"
"endDate" => "2019"
"program" => null
"label" => array:2 [
"fr" => "Statistical Inference and Data Analysis"
"en" => "Statistical Inference and Data Analysis"
]
"type" => array:2 [
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"en" => "Information Systems, Decision Sciences and Statistics"
]
"institution" => array:2 [
"fr" => "University of South California (USC)"
"en" => "University of South California (USC)"
]
"country" => array:2 [
"fr" => "États-Unis"
"en" => "United States of America"
]
]
+lang: "fr"
}
]
"otherActivities" => []
"theses" => []
"indexedAt" => "2024-06-20T02:21:22.000Z"
"contributions" => array:16 [
0 => Essec\Faculty\Model\Contribution {#2217
#_index: "academ_contributions"
#_id: "12571"
#_source: array:18 [
"id" => "12571"
"slug" => "minimax-supervised-clustering-in-the-anisotropic-gaussian-mixture-model-interpolation-is-all-you-need"
"yearMonth" => "2021-07"
"year" => "2021"
"title" => "Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: interpolation is all you need"
"description" => "MINSKER, S., NDAOUD, M. et SHEN, Y. (2021). Minimax Supervised Clustering in the Anisotropic Gaussian Mixture Model: interpolation is all you need. Dans: 2021 Mathematical Statistics and Learning. Barcelona."
"authors" => array:3 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "MINSKER S"
]
2 => array:1 [
"name" => "SHEN Y"
]
]
"ouvrage" => "2021 Mathematical Statistics and Learning"
"keywords" => []
"updatedAt" => "2022-02-10 15:27:48"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"number" => ""
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"type" => array:2 [
"fr" => "Invité dans une conférence académique (Keynote speaker)"
"en" => "Invited speaker at an academic conference"
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"fr" => null
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"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
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}
1 => Essec\Faculty\Model\Contribution {#2219
#_index: "academ_contributions"
#_id: "12664"
#_source: array:18 [
"id" => "12664"
"slug" => "variable-selection-with-hamming-loss"
"yearMonth" => "2018-10"
"year" => "2018"
"title" => "Variable selection with Hamming loss"
"description" => "BUTUCEA, C., NDAOUD, M., STEPANOVA, N. et TSYBAKOV, A.B. (2018). Variable selection with Hamming loss. <i>Annals of Statistics</i>, 46(5), pp. 1837-1875."
"authors" => array:4 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "BUTUCEA Cristina"
]
2 => array:1 [
"name" => "STEPANOVA Natalia"
]
3 => array:1 [
"name" => "TSYBAKOV Alexandre B."
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-01-27 01:00:40"
"publicationUrl" => "https://doi.org/10.1214/17-AOS1572"
"publicationInfo" => array:3 [
"pages" => "1837-1875"
"volume" => "46"
"number" => "5"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
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"support_type" => array:2 [
"fr" => "Revue scientifique"
"en" => "Scientific journal"
]
"countries" => array:2 [
"fr" => null
"en" => null
]
"abstract" => array:2 [
"fr" => "We derive nonasymptotic bounds for the minimax risk of variable selection under expected Hamming loss in the Gaussian mean model."
"en" => "We derive nonasymptotic bounds for the minimax risk of variable selection under expected Hamming loss in the Gaussian mean model."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
2 => Essec\Faculty\Model\Contribution {#2221
#_index: "academ_contributions"
#_id: "12665"
#_source: array:18 [
"id" => "12665"
"slug" => "adaptive-robust-estimation-in-sparse-vector-model"
"yearMonth" => "2021-06"
"year" => "2021"
"title" => "Adaptive robust estimation in sparse vector model"
"description" => "COMMINGES, L., COLLIER, O., NDAOUD, M. et TSYBAKOV, A. (2021). Adaptive robust estimation in sparse vector model. <i>Annals of Statistics</i>, 49(3), pp. 1347-1377."
"authors" => array:4 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "COMMINGES Laëtitia"
]
2 => array:1 [
"name" => "COLLIER Olivier"
]
3 => array:1 [
"name" => "TSYBAKOV Alexandre"
]
]
"ouvrage" => ""
"keywords" => array:6 [
0 => "Adaptive estimation"
1 => "Functional estimation"
2 => "Minimax rate"
3 => "robust estimation"
4 => "Sparse vector model"
5 => "variance estimation"
]
"updatedAt" => "2023-01-27 01:00:40"
"publicationUrl" => "https://doi.org/10.1214/20-AOS2002"
"publicationInfo" => array:3 [
"pages" => "1347-1377"
"volume" => "49"
"number" => "3"
]
"type" => array:2 [
"fr" => "Articles"
"en" => "Journal articles"
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"fr" => null
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]
"abstract" => array:2 [
"fr" => """
For the sparse vector model, we consider estimation of the target vector, of its \n
ℓ\n
2\n
-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet “noise level—noise distribution—sparsity.” We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax nonadaptive rates when the triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the “nominal” distribution in advance we assume that it belongs to some class of distributions.
"""
"en" => """
For the sparse vector model, we consider estimation of the target vector, of its \n
ℓ\n
2\n
-norm and of the noise variance. We construct adaptive estimators and establish the optimal rates of adaptive estimation when adaptation is considered with respect to the triplet “noise level—noise distribution—sparsity.” We consider classes of noise distributions with polynomially and exponentially decreasing tails as well as the case of Gaussian noise. The obtained rates turn out to be different from the minimax nonadaptive rates when the triplet is known. A crucial issue is the ignorance of the noise variance. Moreover, knowing or not knowing the noise distribution can also influence the rate. For example, the rates of estimation of the noise variance can differ depending on whether the noise is Gaussian or sub-Gaussian without a precise knowledge of the distribution. Estimation of noise variance in our setting can be viewed as an adaptive variant of robust estimation of scale in the contamination model, where instead of fixing the “nominal” distribution in advance we assume that it belongs to some class of distributions.
"""
]
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"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
3 => Essec\Faculty\Model\Contribution {#2218
#_index: "academ_contributions"
#_id: "12666"
#_source: array:18 [
"id" => "12666"
"slug" => "optimal-variable-selection-and-adaptive-noisy-compressed-sensing"
"yearMonth" => "2020-04"
"year" => "2020"
"title" => "Optimal variable selection and adaptive noisy Compressed Sensing"
"description" => "NDAOUD, M. et TSYBAKOV, A. (2020). Optimal variable selection and adaptive noisy Compressed Sensing. <i>IEEE Transactions on Information Theory</i>, 66(4), pp. 2517-2532."
"authors" => array:2 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "TSYBAKOV Alexandre"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-01-27 01:00:40"
"publicationUrl" => "https://ieeexplore.ieee.org/document/8955982"
"publicationInfo" => array:3 [
"pages" => "2517-2532"
"volume" => "66"
"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" => "In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed standard Gaussian. This algorithm achieves the same conditions of exact recovery as the exhaustive search (maximal likelihood) decoder, and has an advantage over the latter of being adaptive to all parameters of the problem and computable in polynomial time. The core of our analysis consists in the study of the non-asymptotic minimax Hamming risk of variable selection. This allows us to derive a procedure, which is nearly optimal in a non-asymptotic minimax sense. Then, we develop its adaptive version, and propose a robust variant of the method to handle datasets with outliers and heavy-tailed distributions of observations. The resulting polynomial time procedure is near optimal, adaptive to all parameters of the problem and also robust."
"en" => "In the context of high-dimensional linear regression models, we propose an algorithm of exact support recovery in the setting of noisy compressed sensing where all entries of the design matrix are independent and identically distributed standard Gaussian. This algorithm achieves the same conditions of exact recovery as the exhaustive search (maximal likelihood) decoder, and has an advantage over the latter of being adaptive to all parameters of the problem and computable in polynomial time. The core of our analysis consists in the study of the non-asymptotic minimax Hamming risk of variable selection. This allows us to derive a procedure, which is nearly optimal in a non-asymptotic minimax sense. Then, we develop its adaptive version, and propose a robust variant of the method to handle datasets with outliers and heavy-tailed distributions of observations. The resulting polynomial time procedure is near optimal, adaptive to all parameters of the problem and also robust."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
4 => Essec\Faculty\Model\Contribution {#2222
#_index: "academ_contributions"
#_id: "12667"
#_source: array:18 [
"id" => "12667"
"slug" => "interplay-of-minimax-estimation-and-minimax-support-recovery-under-sparsity"
"yearMonth" => "2019-03"
"year" => "2019"
"title" => "Interplay of minimax estimation and minimax support recovery under sparsity"
"description" => "NDAOUD, M. (2019). Interplay of minimax estimation and minimax support recovery under sparsity. Dans: <i>Algorithmic Learning Theory (ALT)</i>. Proceedings of Machine Learning Research."
"authors" => array:1 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
]
"ouvrage" => "Algorithmic Learning Theory (ALT)"
"keywords" => []
"updatedAt" => "2023-01-27 01:00:40"
"publicationUrl" => null
"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" => "Royaume-Uni"
"en" => "United Kingdom"
]
"abstract" => array:2 [
"fr" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
5 => Essec\Faculty\Model\Contribution {#2216
#_index: "academ_contributions"
#_id: "12730"
#_source: array:18 [
"id" => "12730"
"slug" => "improved-clustering-algorithms-for-the-bipartite-stochastic-block-model"
"yearMonth" => "2022-03"
"year" => "2022"
"title" => "Improved clustering algorithms for the Bipartite Stochastic Block Model"
"description" => "NDAOUD, M., SIGALA, S. et TSYBAKOV, A. (2022). Improved clustering algorithms for the Bipartite Stochastic Block Model. <i>IEEE Transactions on Information Theory</i>, 68(3), pp. 1960-1975."
"authors" => array:3 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "SIGALA Suzanne"
]
2 => array:1 [
"name" => "TSYBAKOV Alexandre"
]
]
"ouvrage" => ""
"keywords" => array:6 [
0 => "Bipartite Stochastic Block Model"
1 => "exact recovery"
2 => "almost full recovery"
3 => "spectral methods"
4 => "clustering"
5 => "phase transition"
]
"updatedAt" => "2023-05-24 16:29:20"
"publicationUrl" => "https://arxiv.org/pdf/1911.07987.pdf"
"publicationInfo" => array:3 [
"pages" => "1960-1975"
"volume" => "68"
"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 establish sufficient conditions of exact and almost full recovery of the node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time algorithms. First, we improve upon the known conditions of almost full recovery by spectral clustering algorithms in BSBM. Next, we propose a new computationally simple and fast procedure achieving exact recovery under milder conditions than the state of the art. Namely, if the vertex sets $V_1$ and $V_2$ in BSBM have sizes $n_1$ and $n_2$, we show that the condition \n
p = \Omega\left(\max\left(\sqrt{\frac{\log{n_1}}{n_1n_2}},\frac{\log{n_1}}{n_2}\right)\right) $ on the edge intensity $p$ is sufficient for exact recovery witin $V_1$. This condition exhibits an elbow at $n_{2} \asymp n_1\log{n_1}$ between the low-dimensional and high-dimensional regimes. The suggested procedure is a variant of Lloyd's iterations initialized with a well-chosen spectral estimator leading to what we expect to be the optimal condition for exact recovery in BSBM. {The optimality conjecture is supported by showing that, for a supervised oracle procedure, such a condition is necessary to achieve exact recovery.} The key elements of the proof techniques are different from classical community detection tools on random graphs. Numerical studies confirm our theory, and show that the suggested algorithm is both very fast and achieves {almost the same} performance as the supervised oracle. Finally, using the connection between planted satisfiability problems and the BSBM, we improve upon the sufficient number of clauses to completely recover the planted assignment.
"""
"en" => """
We establish sufficient conditions of exact and almost full recovery of the node partition in Bipartite Stochastic Block Model (BSBM) using polynomial time algorithms. First, we improve upon the known conditions of almost full recovery by spectral clustering algorithms in BSBM. Next, we propose a new computationally simple and fast procedure achieving exact recovery under milder conditions than the state of the art. Namely, if the vertex sets $V_1$ and $V_2$ in BSBM have sizes $n_1$ and $n_2$, we show that the condition \n
p = \Omega\left(\max\left(\sqrt{\frac{\log{n_1}}{n_1n_2}},\frac{\log{n_1}}{n_2}\right)\right) $ on the edge intensity $p$ is sufficient for exact recovery witin $V_1$. This condition exhibits an elbow at $n_{2} \asymp n_1\log{n_1}$ between the low-dimensional and high-dimensional regimes. The suggested procedure is a variant of Lloyd's iterations initialized with a well-chosen spectral estimator leading to what we expect to be the optimal condition for exact recovery in BSBM. {The optimality conjecture is supported by showing that, for a supervised oracle procedure, such a condition is necessary to achieve exact recovery.} The key elements of the proof techniques are different from classical community detection tools on random graphs. Numerical studies confirm our theory, and show that the suggested algorithm is both very fast and achieves {almost the same} performance as the supervised oracle. Finally, using the connection between planted satisfiability problems and the BSBM, we improve upon the sufficient number of clauses to completely recover the planted assignment.
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
6 => Essec\Faculty\Model\Contribution {#2220
#_index: "academ_contributions"
#_id: "12752"
#_source: array:18 [
"id" => "12752"
"slug" => "robust-and-efficient-mean-estimation-an-approach-based-on-the-properties-of-self-normalized-sums"
"yearMonth" => "2021-12"
"year" => "2021"
"title" => "Robust and efficient mean estimation: an approach based on the properties of self-normalized sums"
"description" => "MINSKER, S. et NDAOUD, M. (2021). Robust and efficient mean estimation: an approach based on the properties of self-normalized sums. <i>The Electronic Journal of Statistics</i>, 15(2), pp. 6036-6070."
"authors" => array:2 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "MINSKER Stanislav"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "efficiency"
1 => "robust estimation"
2 => "self-normalized sums"
3 => "sub-Gaussian deviations"
]
"updatedAt" => "2023-07-10 16:47:23"
"publicationUrl" => "https://projecteuclid.org/journals/electronic-journal-of-statistics/volume-15/issue-2/Robust-and-efficient-mean-estimation--an-approach-based-on/10.1214/21-EJS1925.full"
"publicationInfo" => array:3 [
"pages" => "6036-6070"
"volume" => "15"
"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" => "Let X be a random variable with unknown mean and finite variance. We present a new estimator of the mean of X that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation guarantees without any additional assumptions on the shape or tails of the distribution, and moreover is asymptotically efficient. This is the first estimator that provably combines all these qualities in one package. Our construction is inspired by robustness properties possessed by the self-normalized sums. Theoretical findings are supplemented by numerical simulations highlighting strong performance of the proposed estimator in comparison with previously known techniques."
"en" => "Let X be a random variable with unknown mean and finite variance. We present a new estimator of the mean of X that is robust with respect to the possible presence of outliers in the sample, provides tight sub-Gaussian deviation guarantees without any additional assumptions on the shape or tails of the distribution, and moreover is asymptotically efficient. This is the first estimator that provably combines all these qualities in one package. Our construction is inspired by robustness properties possessed by the self-normalized sums. Theoretical findings are supplemented by numerical simulations highlighting strong performance of the proposed estimator in comparison with previously known techniques."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
7 => Essec\Faculty\Model\Contribution {#2223
#_index: "academ_contributions"
#_id: "12816"
#_source: array:18 [
"id" => "12816"
"slug" => "sharp-optimal-recovery-in-the-two-component-gaussian-mixture-model"
"yearMonth" => "2022-02"
"year" => "2022"
"title" => "Sharp optimal recovery in the two Component Gaussian Mixture Model"
"description" => "NDAOUD, M. (2022). Sharp optimal recovery in the two Component Gaussian Mixture Model. <i>Annals of Statistics</i>, 50(4), pp. 2096-2126."
"authors" => array:1 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-07-10 17:16:12"
"publicationUrl" => "https://projecteuclid.org/journals/annals-of-statistics/volume-50/issue-4/Sharp-optimal-recovery-in-the-two-component-Gaussian-mixture-model/10.1214/22-AOS2178.short"
"publicationInfo" => array:3 [
"pages" => "2096-2126"
"volume" => "50"
"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" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
8 => Essec\Faculty\Model\Contribution {#2224
#_index: "academ_contributions"
#_id: "13137"
#_source: array:18 [
"id" => "13137"
"slug" => "harmonic-analysis-meets-stationarity-a-general-framework-for-series-expansions-of-special-gaussian-processes"
"yearMonth" => "2023-05"
"year" => "2023"
"title" => "Harmonic analysis meets stationarity: A general framework for series expansions of special Gaussian processes"
"description" => "NDAOUD, M. (2023). Harmonic analysis meets stationarity: A general framework for series expansions of special Gaussian processes. <i>Bernoulli: A Journal of Mathematical Statistics and Probability</i>, 29(3), pp. 2295 - 2317."
"authors" => array:1 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2023-07-04 17:03:16"
"publicationUrl" => "https://projecteuclid.org/journals/bernoulli/volume-29/issue-3/Harmonic-analysis-meets-stationarity--A-general-framework-for-series/10.3150/22-BEJ1542.short"
"publicationInfo" => array:3 [
"pages" => "2295 - 2317"
"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" => """
In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their\n
covariance function. In particular, we propose a new simple rate-optimal\n
series expansion for fractional Brownian motion. The convergence of the\n
latter series holds in mean square and uniformly almost surely, with a rateoptimal decay of the remainder of the series. We also develop a general\n
framework of convergent series expansions for certain classes of Gaussian\n
processes with stationarity. Finally, an application to optimal functional\n
quantization is described.
"""
"en" => """
In this paper, we present a new approach to derive series expansions for some Gaussian processes based on harmonic analysis of their\n
covariance function. In particular, we propose a new simple rate-optimal\n
series expansion for fractional Brownian motion. The convergence of the\n
latter series holds in mean square and uniformly almost surely, with a rateoptimal decay of the remainder of the series. We also develop a general\n
framework of convergent series expansions for certain classes of Gaussian\n
processes with stationarity. Finally, an application to optimal functional\n
quantization is described.
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
9 => Essec\Faculty\Model\Contribution {#2225
#_index: "academ_contributions"
#_id: "13927"
#_source: array:18 [
"id" => "13927"
"slug" => "variable-selection-monotone-likelihood-ratio-and-group-sparsity"
"yearMonth" => "2023-02"
"year" => "2023"
"title" => "Variable selection, monotone likelihood ratio and group sparsity"
"description" => "BUTUCEA, C., MAMMEN, E., NDAOUD, M. et TSYBAKOV, A.B. (2023). Variable selection, monotone likelihood ratio and group sparsity. <i>Annals of Statistics</i>, 51(1), pp. 312-333."
"authors" => array:4 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "BUTUCEA Cristina"
]
2 => array:1 [
"name" => "MAMMEN Enno"
]
3 => array:1 [
"name" => "TSYBAKOV Alexandre B."
]
]
"ouvrage" => ""
"keywords" => array:8 [
0 => "almost full recovery"
1 => "exact recovery"
2 => "group variable selection"
3 => "Hamming loss"
4 => "minimax risk"
5 => "pivotal selection problem"
6 => "Sparsity"
7 => "Variable selection"
]
"updatedAt" => "2023-07-10 16:46:17"
"publicationUrl" => "https://projecteuclid.org/journals/annals-of-statistics/volume-51/issue-1/Variable-selection-monotone-likelihood-ratio-and-group-sparsity/10.1214/22-AOS2251.short"
"publicationInfo" => array:3 [
"pages" => "312-333"
"volume" => "51"
"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" => "In the pivotal variable selection problem, we derive the exact nonasymptotic minimax selector over the class of all s-sparse vectors, which is also the Bayes selector with respect to the uniform prior. While this optimal selector is, in general, not realizable in polynomial time, we show that its tractable counterpart (the scan selector) attains the minimax expected Hamming risk to within factor 2, and is also exact minimax with respect to the probability of wrong recovery. As a consequence, we establish explicit lower bounds under the monotone likelihood ratio property and we obtain a tight characterization of the minimax risk in terms of the best separable selector risk. We apply these general results to derive necessary and sufficient conditions of exact and almost full recovery in the location model with light tail distributions and in the problem of group variable selection under Gaussian noise and under more general anisotropic sub-Gaussian noise. Numerical results illustrate our theoretical findings."
"en" => "In the pivotal variable selection problem, we derive the exact nonasymptotic minimax selector over the class of all s-sparse vectors, which is also the Bayes selector with respect to the uniform prior. While this optimal selector is, in general, not realizable in polynomial time, we show that its tractable counterpart (the scan selector) attains the minimax expected Hamming risk to within factor 2, and is also exact minimax with respect to the probability of wrong recovery. As a consequence, we establish explicit lower bounds under the monotone likelihood ratio property and we obtain a tight characterization of the minimax risk in terms of the best separable selector risk. We apply these general results to derive necessary and sufficient conditions of exact and almost full recovery in the location model with light tail distributions and in the problem of group variable selection under Gaussian noise and under more general anisotropic sub-Gaussian noise. Numerical results illustrate our theoretical findings."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
10 => Essec\Faculty\Model\Contribution {#2226
#_index: "academ_contributions"
#_id: "14223"
#_source: array:18 [
"id" => "14223"
"slug" => "adaptive-robust-and-sub-gaussian-deviations-in-sparse-linear-regression"
"yearMonth" => "2022-12"
"year" => "2022"
"title" => "Adaptive Robust and Sub-Gaussian Deviations in Sparse Linear Regression"
"description" => "NDAOUD, M. et MINSKER, S. (2022). Adaptive Robust and Sub-Gaussian Deviations in Sparse Linear Regression. Dans: 2022 Institute of Mathematical Statistics (IMS) International Conference on Statistics and Data Science (ICSDS). Florence."
"authors" => array:2 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "MINSKER S."
]
]
"ouvrage" => "2022 Institute of Mathematical Statistics (IMS) International Conference on Statistics and Data Science (ICSDS)"
"keywords" => []
"updatedAt" => "2023-07-21 01:00:39"
"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, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
11 => Essec\Faculty\Model\Contribution {#2227
#_index: "academ_contributions"
#_id: "14224"
#_source: array:18 [
"id" => "14224"
"slug" => "variable-selection-monotone-likelihood-ratio-and-group-sparsity"
"yearMonth" => "2022-06"
"year" => "2022"
"title" => "Variable selection, monotone likelihood ratio and group sparsity"
"description" => "BUTUCEA, C., MAMMEN, E., NDAOUD, M. et TSYBAKOV, A.B. (2022). Variable selection, monotone likelihood ratio and group sparsity. Dans: 2022 Institute of Mathematical Statistics (IMS) Annual Meeting. London."
"authors" => array:4 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "BUTUCEA Cristina"
]
2 => array:1 [
"name" => "MAMMEN Enno"
]
3 => array:1 [
"name" => "TSYBAKOV Alexandre B."
]
]
"ouvrage" => "2022 Institute of Mathematical Statistics (IMS) Annual Meeting"
"keywords" => []
"updatedAt" => "2023-07-21 01:00:39"
"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, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
12 => Essec\Faculty\Model\Contribution {#2228
#_index: "academ_contributions"
#_id: "14225"
#_source: array:18 [
"id" => "14225"
"slug" => "adaptive-robustness-and-sub-gaussian-deviations-in-sparse-linear-regression-through-pivotal-double-slope"
"yearMonth" => "2022-05"
"year" => "2022"
"title" => "Adaptive Robustness and sub-Gaussian Deviations in Sparse Linear Regression through Pivotal Double SLOPE"
"description" => "NDAOUD, M. et MINSKER, S. (2022). Adaptive Robustness and sub-Gaussian Deviations in Sparse Linear Regression through Pivotal Double SLOPE. Dans: Re-thinking High-dimensional Mathematical Statistics. Oberwolfach."
"authors" => array:2 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "MINSKER S."
]
]
"ouvrage" => "Re-thinking High-dimensional Mathematical Statistics"
"keywords" => []
"updatedAt" => "2023-07-21 01:00:39"
"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, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
13 => Essec\Faculty\Model\Contribution {#2229
#_index: "academ_contributions"
#_id: "14667"
#_source: array:18 [
"id" => "14667"
"slug" => "robust-and-tuning-free-sparse-linear-regression-via-square-root-slope"
"yearMonth" => "2024-01"
"year" => "2024"
"title" => "Robust and Tuning-Free Sparse Linear Regression via Square-Root Slope"
"description" => "NDAOUD, M., MINSKER, S. et WANG, L. (2024). Robust and Tuning-Free Sparse Linear Regression via Square-Root Slope. Dans: 6th Institute for Mathematical Statistics – Asia-Pacific Rim Meeting (IMS-APRM 2024). Melbourne."
"authors" => array:3 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "MINSKER Stanislav"
]
2 => array:1 [
"name" => "WANG Lang"
]
]
"ouvrage" => "6th Institute for Mathematical Statistics – Asia-Pacific Rim Meeting (IMS-APRM 2024)"
"keywords" => []
"updatedAt" => "2024-01-31 01:00:38"
"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, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
14 => Essec\Faculty\Model\Contribution {#2230
#_index: "academ_contributions"
#_id: "14668"
#_source: array:18 [
"id" => "14668"
"slug" => "robust-and-efficient-mean-estimation-an-approach-based-on-the-properties-of-self-normalized-sums"
"yearMonth" => "2023-12"
"year" => "2023"
"title" => "Robust and Efficient Mean Estimation: an Approach Based on the Properties of Self-Normalized Sums"
"description" => "NDAOUD, M. et MINSKER, S. (2023). Robust and Efficient Mean Estimation: an Approach Based on the Properties of Self-Normalized Sums. Dans: 2023 Mathematics & Decision Conference. Ben Guerir."
"authors" => array:2 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "MINSKER Stanislav "
]
]
"ouvrage" => "2023 Mathematics & Decision Conference"
"keywords" => []
"updatedAt" => "2024-01-31 01:00:38"
"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" => ""
]
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"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
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}
15 => Essec\Faculty\Model\Contribution {#2231
#_index: "academ_contributions"
#_id: "14831"
#_source: array:18 [
"id" => "14831"
"slug" => "robust-and-tuning-free-sparse-linear-regression-via-square-root-slope"
"yearMonth" => "2024-05"
"year" => "2024"
"title" => "Robust and Tuning-Free Sparse Linear Regression via Square-Root Slope"
"description" => "MINSKER, S., NDAOUD, M. et WANG, L. (2024). Robust and Tuning-Free Sparse Linear Regression via Square-Root Slope. <i>SIAM Journal on Mathematics of Data Science</i>, 6(2), pp. 428-453."
"authors" => array:3 [
0 => array:3 [
"name" => "NDAOUD Mohamed"
"bid" => "B00791786"
"slug" => "ndaoud-mohamed"
]
1 => array:1 [
"name" => "Minsker Stanislav"
]
2 => array:1 [
"name" => "Wang Lang"
]
]
"ouvrage" => ""
"keywords" => array:4 [
0 => "robust inference"
1 => "sub-Gaussian deviations"
2 => "Slope"
3 => "sparse linear regression"
]
"updatedAt" => "2024-06-03 13:28:02"
"publicationUrl" => "https://doi.org/10.1137/23M1608690"
"publicationInfo" => array:3 [
"pages" => "428-453"
"volume" => "6"
"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" => "We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where dense additive noise is heavy-tailed, while the measurement vectors follow a sub-Gaussian distribution. Within this framework, we establish minimax lower bounds for the performance of an arbitrary estimator that depend on the fraction of corrupted observations as well as the tail behavior of the additive noise. Moreover, we design a modification of the so-called square-root Slope estimator with several desirable features: (a) It is provably robust to adversarial contamination and satisfies performance guarantees in the form of sub-Gaussian deviation inequalities that match the lower error bounds, up to logarithmic factors; (b) it is fully adaptive with respect to the unknown sparsity level and the variance of the additive noise; and (c) it is computationally tractable as a solution of a convex optimization problem. To analyze performance of the proposed estimator, we prove several properties of matrices with sub-Gaussian rows that may be of independent interest."
"en" => "We consider the high-dimensional linear regression model and assume that a fraction of the measurements are altered by an adversary with complete knowledge of the data and the underlying distribution. We are interested in a scenario where dense additive noise is heavy-tailed, while the measurement vectors follow a sub-Gaussian distribution. Within this framework, we establish minimax lower bounds for the performance of an arbitrary estimator that depend on the fraction of corrupted observations as well as the tail behavior of the additive noise. Moreover, we design a modification of the so-called square-root Slope estimator with several desirable features: (a) It is provably robust to adversarial contamination and satisfies performance guarantees in the form of sub-Gaussian deviation inequalities that match the lower error bounds, up to logarithmic factors; (b) it is fully adaptive with respect to the unknown sparsity level and the variance of the additive noise; and (c) it is computationally tractable as a solution of a convex optimization problem. To analyze performance of the proposed estimator, we prove several properties of matrices with sub-Gaussian rows that may be of independent interest."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d’Information, Sciences de la Décision et Statistiques"
"en" => "Information Systems, Decision Sciences and Statistics"
]
"indexedAt" => "2024-06-20T02:21:55.000Z"
]
+lang: "fr"
+"_type": "_doc"
+"_score": 6.4440417
+"parent": null
}
]
"avatar" => "https://faculty.essec.edu/wp-content/uploads/avatars/B00791786.jpg"
"contributionCounts" => 16
"personalLinks" => array:2 [
0 => "<a href="https://orcid.org/0000-0002-0255-9815" target="_blank">ORCID</a>"
1 => "<a href="https://scholar.google.fr/citations?user=aZ2SLH8AAAAJ&hl=fr" target="_blank">Google scholar</a>"
]
"docTitle" => "Mohamed NDAOUD"
"docSubtitle" => "Professeur assistant"
"docDescription" => "Département: Systèmes d’information, sciences de la décision et statistiques<br>Campus de Cergy"
"docType" => "cv"
"docPreview" => "<img src="https://faculty.essec.edu/wp-content/uploads/avatars/B00791786.jpg"><span><span>Mohamed NDAOUD</span><span>B00791786</span></span>"
]
#_index: "academ_cv"
+lang: "fr"
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+"parent": null
}