Essec\Faculty\Model\Profile {#2189
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]
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"campus" => "Campus de Cergy"
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0 => Essec\Faculty\Model\CareerItem {#2190
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}
1 => Essec\Faculty\Model\CareerItem {#2194
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}
2 => Essec\Faculty\Model\CareerItem {#2188
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3 => Essec\Faculty\Model\CareerItem {#2192
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4 => Essec\Faculty\Model\CareerItem {#2195
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5 => Essec\Faculty\Model\CareerItem {#2196
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6 => Essec\Faculty\Model\CareerItem {#2197
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0 => Essec\Faculty\Model\Diplome {#2191
#_index: null
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]
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}
1 => Essec\Faculty\Model\Diplome {#2193
#_index: null
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"diplome" => "DIPLOMA"
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"fr" => "Master of Science, Mathematics, Operational Research, Statistics and Economics"
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"en" => "University of Warwick"
]
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"fr" => "Royaume-Uni"
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]
]
+lang: "en"
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}
]
"bio" => array:2 [
"fr" => "<p>Mikołaj est professeure assistant à l’ESSEC. Mikołaj a obtenu son BSc et son MSc à l'Université de Warwick, puis son doctorat en statistiques à l'Université d'Oxford. Après avoir terminé son doctorat, il rejoint le département de mathématiques de l'Université du Luxembourg en tant que chercheur postdoctoral. Ensuite, il décroche la bourse individuelle Marie Skłodowska-Curie, parrainée par l'Union européenne. Lors du début de la bourse, il a travaillé au Laboratoire des systèmes d'information et de décision du MIT et a effectué une brève mission au Gatsby Computational Neuroscience Unit à l'University College de Londres (UCL). Il est ensuite retourné au Luxembourg pour la fin de la bourse, après quoi il a rejoint l'ESSEC. Ses recherches portent sur l’apport de garanties de qualité rigoureuses pour diverses approximations dans les domaines de la probabilité appliquée, des statistiques et de l'apprentissage automatique.</p>\n"
"en" => """
<p dir="ltr"><span style="background-color:transparent; color:rgb(20, 27, 77)">Mikołaj is a tenure-track assistant professor at ESSEC Business School, specializing in mathematical statistics and applied probability. He obtained his Bachelor’s and Master’s degree in Mathematics, Operational Research, Statistics and Economics from the University of Warwick in the UK and his DPhil in Statistics from the University of Oxford. After his DPhil, he joined the Mathematics Department at the University of Luxembourg as a postdoctoral research associate. Later, he obtained a Marie Skłodowska-Curie Individual (Global) Fellowship, sponsored by the EU. </span></p>\n
\n
<p dir="ltr"><span style="background-color:transparent; color:rgb(20, 27, 77)">During the outgoing phase of the fellowship, he worked at the Laboratory for Information and Decision Systems at the Massachusetts Institute of Technology (MIT) and undertook a short secondment at the Gatsby Computational Neuroscience Unit at University College London (UCL). He then returned to Luxembourg for the incoming phase of the fellowhip, after which he joined ESSEC in 2024.</span></p>\n
\n
<p dir="ltr"><span style="background-color:transparent; color:rgb(20, 27, 77)">In his research, Mikołaj is interested in providing rigorous quality guarantees for various approximations arising in applied probability, statistics and machine learning. Along the way, he develops new mathematical theory and tools for upper-bounding distances between probability distributions. He enjoys working on theoretical problems and proving new theorems which are motivated by real-life applications.</span></p>\n
\n
<p> </p>\n
"""
]
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0 => Essec\Faculty\Model\Distinction {#2198
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"fr" => "Marie Skłodowska-Curie Individual (Global) Fellowship"
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]
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}
1 => Essec\Faculty\Model\Distinction {#2199
#_index: null
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"date" => "2019-04-01"
"label" => array:2 [
"fr" => "New Researcher Travel Award"
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}
2 => Essec\Faculty\Model\Distinction {#2200
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}
3 => Essec\Faculty\Model\Distinction {#2201
#_index: null
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"date" => "2015-10-01"
"label" => array:2 [
"fr" => "Full Doctoral Studentship"
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"teaching" => []
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0 => Essec\Faculty\Model\Contribution {#2203
#_index: "academ_contributions"
#_id: "15106"
#_source: array:18 [
"id" => "15106"
"slug" => "note-on-a-barbours-paper-on-steins-method-for-diffusion-approximations"
"yearMonth" => "2017-04"
"year" => "2017"
"title" => "Note on A. Barbour’s paper on Stein’s method for diffusion approximations"
"description" => "KASPRZAK, M., DUNCAN, A.B. et VOLLMER, S.J. (2017). Note on A. Barbour’s paper on Stein’s method for diffusion approximations. <i>Electronic Communications in Probability</i>, 22, pp. 1-8."
"authors" => array:3 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "Duncan Andrew B."
]
2 => array:1 [
"name" => "Vollmer Sebastian J."
]
]
"ouvrage" => ""
"keywords" => array:3 [
0 => "diffusion approximations"
1 => "Donsker’s theorem"
2 => "Stein’s method"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/17-ECP54"
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"pages" => "1-8"
"volume" => "22"
"number" => null
]
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"abstract" => array:2 [
"fr" => """
In [2] foundations for diffusion approximation via Stein’s method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein’s method (see, for example, its use in [1] or [7]). A semigroup argument is used in [2] to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in [2], the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on \n
D\n
[\n
0\n
,\n
1\n
]\n
growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of [2] hold true.
"""
"en" => """
In [2] foundations for diffusion approximation via Stein’s method are laid. This paper has been cited more than 130 times and is a cornerstone in the area of Stein’s method (see, for example, its use in [1] or [7]). A semigroup argument is used in [2] to solve a Stein equation for Gaussian diffusion approximation. We prove that, contrary to the claim in [2], the semigroup considered therein is not strongly continuous on the Banach space of continuous, real-valued functions on \n
D\n
[\n
0\n
,\n
1\n
]\n
growing slower than a cubic, equipped with an appropriate norm. We also provide a proof of the exact formulation of the solution to the Stein equation of interest, which does not require the aforementioned strong continuity. This shows that the main results of [2] hold true.
"""
]
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"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
1 => Essec\Faculty\Model\Contribution {#2205
#_index: "academ_contributions"
#_id: "15107"
#_source: array:18 [
"id" => "15107"
"slug" => "scalable-gaussian-process-inference-with-finite-data-mean-and-variance-guarantees"
"yearMonth" => "2019-04"
"year" => "2019"
"title" => "Scalable Gaussian Process Inference with Finite-data Mean and Variance Guarantees"
"description" => "HUGGINS, J.H., CAMPBELL, T., KASPRZAK, M. et BRODERICK, T. (2019). Scalable Gaussian Process Inference with Finite-data Mean and Variance Guarantees. Dans: <i>22nd International Conference on Artificial Intelligence and Statistics (AISTATS)</i>. Proceedings of Machine Learning Research."
"authors" => array:4 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "HUGGINS Jonathan H."
]
2 => array:1 [
"name" => "CAMPBELL Trevor"
]
3 => array:1 [
"name" => "BRODERICK Tamara"
]
]
"ouvrage" => "22nd International Conference on Artificial Intelligence and Statistics (AISTATS)"
"keywords" => []
"updatedAt" => "2024-09-17 15:51:33"
"publicationUrl" => "https://proceedings.mlr.press/v89/huggins19a.html"
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"pages" => ""
"volume" => "89"
"number" => ""
]
"type" => array:2 [
"fr" => "Actes d'une conférence"
"en" => "Conference Proceedings"
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"fr" => "Collection"
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"fr" => null
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"abstract" => array:2 [
"fr" => ""
"en" => ""
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"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
2 => Essec\Faculty\Model\Contribution {#2207
#_index: "academ_contributions"
#_id: "15108"
#_source: array:18 [
"id" => "15108"
"slug" => "steins-method-for-multivariate-brownian-approximations-of-sums-under-dependence"
"yearMonth" => "2020-08"
"year" => "2020"
"title" => "Stein’s method for multivariate Brownian approximations of sums under dependence"
"description" => "KASPRZAK, M. (2020). Stein’s method for multivariate Brownian approximations of sums under dependence. <i>Stochastic Processes and their Applications</i>, 130(8), pp. 4927-4967."
"authors" => array:1 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
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"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-09-09 11:28:52"
"publicationUrl" => "https://doi.org/10.1016/j.spa.2020.02.006"
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"pages" => "4927-4967"
"volume" => "130"
"number" => "8"
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"abstract" => array:2 [
"fr" => "We use Stein’s method to obtain a bound on the distance between scaled p-dimensional random walks and a p-dimensional (correlated) Brownian motion. We consider dependence schemes including those in which the summands in scaled sums are weakly dependent and their p components are strongly correlated. As an example application, we prove a functional limit theorem for exceedances in an m-scans process, together with a bound on the rate of convergence. We also find a bound on the rate of convergence of scaled U-statistics to Brownian motion, representing an example of a sum of strongly dependent terms."
"en" => "We use Stein’s method to obtain a bound on the distance between scaled p-dimensional random walks and a p-dimensional (correlated) Brownian motion. We consider dependence schemes including those in which the summands in scaled sums are weakly dependent and their p components are strongly correlated. As an example application, we prove a functional limit theorem for exceedances in an m-scans process, together with a bound on the rate of convergence. We also find a bound on the rate of convergence of scaled U-statistics to Brownian motion, representing an example of a sum of strongly dependent terms."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
3 => Essec\Faculty\Model\Contribution {#2204
#_index: "academ_contributions"
#_id: "15109"
#_source: array:18 [
"id" => "15109"
"slug" => "functional-approximations-via-steins-method-of-exchangeable-pairs"
"yearMonth" => "2020-11"
"year" => "2020"
"title" => "Functional approximations via Stein’s method of exchangeable pairs"
"description" => "KASPRZAK, M. (2020). Functional approximations via Stein’s method of exchangeable pairs. <i>Annales de l Institut Henri Poincare-Probabilites et Statistiques</i>, 56(4)."
"authors" => array:1 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
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"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/20-AIHP1049"
"publicationInfo" => array:3 [
"pages" => null
"volume" => "56"
"number" => "4"
]
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"abstract" => array:2 [
"fr" => "Nous combinons la méthode des paires échangeables avec la méthode d’approximation fonctionnelle de Stein. De cette façon, nous obtenons une condition générale de linéarité sous laquelle un résultat abstrait d’approximation Gaussienne est valide. Nous appliquons cette approche à l’estimation de la distance entre une somme de variables aléatoires, choisies dans un tableau par le biais d’une permutation aléatoire, et un mélange de processus Gaussiens. À partir de ce résultat, nous prouvons un théorème central limite fonctionnel combinatoire. Nous considérons également un graphe aléatoire et fournissons des bornes pour la vitesse de convergence de la loi de son nombre d’arêtes (aprés un changement d’échelle) vers un processus Gaussien continu."
"en" => "We combine the method of exchangeable pairs with Stein’s method for functional approximation. As a result, we give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply this approach to estimate the distance of a sum of random variables, chosen from an array according to a random permutation, from a Gaussian mixture process. This result lets us prove a functional combinatorial central limit theorem. We also consider a graph-valued process and bound the speed of convergence of the distribution of its rescaled edge counts to a continuous Gaussian process."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
4 => Essec\Faculty\Model\Contribution {#2208
#_index: "academ_contributions"
#_id: "15110"
#_source: array:18 [
"id" => "15110"
"slug" => "steins-method-of-exchangeable-pairs-in-multivariate-functional-approximations"
"yearMonth" => "2021-03"
"year" => "2021"
"title" => "Stein’s method of exchangeable pairs in multivariate functional approximations"
"description" => "DÖBLER, C. et KASPRZAK, M. (2021). Stein’s method of exchangeable pairs in multivariate functional approximations. <i>Electronic Journal of Probability</i>, 26, pp. 1-50."
"authors" => array:2 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "Döbler Christian"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/21-EJP587"
"publicationInfo" => array:3 [
"pages" => "1-50"
"volume" => "26"
"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" => "In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by Barbour (1990) and Kasprzak (2020). We demonstrate the applicability of our results by applying them to joint subgraph counts in an Erdős-Renyi random graph model on the one hand and to vectors of weighted, degenerate U-processes on the other hand. As a concrete instance of the latter class of examples, we provide a bound for the functional approximation of a vector of success runs of different lengths by a suitable Gaussian process which, even in the situation of just a single run, would be outside the scope of the existing theory."
"en" => "In this paper we develop a framework for multivariate functional approximation by a suitable Gaussian process via an exchangeable pairs coupling that satisfies a suitable approximate linear regression property, thereby building on work by Barbour (1990) and Kasprzak (2020). We demonstrate the applicability of our results by applying them to joint subgraph counts in an Erdős-Renyi random graph model on the one hand and to vectors of weighted, degenerate U-processes on the other hand. As a concrete instance of the latter class of examples, we provide a bound for the functional approximation of a vector of success runs of different lengths by a suitable Gaussian process which, even in the situation of just a single run, would be outside the scope of the existing theory."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
5 => Essec\Faculty\Model\Contribution {#2202
#_index: "academ_contributions"
#_id: "15111"
#_source: array:18 [
"id" => "15111"
"slug" => "functional-convergence-of-sequential-u-processes-with-size-dependent-kernels"
"yearMonth" => "2022-02"
"year" => "2022"
"title" => "Functional convergence of sequential U-processes with size-dependent kernels"
"description" => "DÖBLER, C., KASPRZAK, M. et PECCATI, G. (2022). Functional convergence of sequential U-processes with size-dependent kernels. <i>Annals of Applied Probability</i>, 32(1), pp. 551-601."
"authors" => array:3 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "Döbler Christian"
]
2 => array:1 [
"name" => "Peccati Giovanni"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org//10.1214/21-AAP1688"
"publicationInfo" => array:3 [
"pages" => "551-601"
"volume" => "32"
"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 consider sequences of U-processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of analytic sufficient conditions, under which the aforementioned U-processes weakly converge to a linear combination of time-changed independent Brownian motions. In view of the underlying symmetric structure, the involved time-changes and weights remarkably depend only on the order of the U-statistic, and have consequently a universal nature."
"en" => "We consider sequences of U-processes based on symmetric kernels of a fixed order, that possibly depend on the sample size. Our main contribution is the derivation of a set of analytic sufficient conditions, under which the aforementioned U-processes weakly converge to a linear combination of time-changed independent Brownian motions. In view of the underlying symmetric structure, the involved time-changes and weights remarkably depend only on the order of the U-statistic, and have consequently a universal nature."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
6 => Essec\Faculty\Model\Contribution {#2206
#_index: "academ_contributions"
#_id: "15112"
#_source: array:18 [
"id" => "15112"
"slug" => "the-multivariate-functional-de-jong-clt"
"yearMonth" => "2022-10"
"year" => "2022"
"title" => "The multivariate functional de Jong CLT"
"description" => "DÖBLER, C., KASPRZAK, M. et PECCATI, G. (2022). The multivariate functional de Jong CLT. <i>Probability Theory and Related Fields</i>, 184(1-2), pp. 367-399."
"authors" => array:3 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "Döbler Christian"
]
2 => array:1 [
"name" => "Peccati Giovanni"
]
]
"ouvrage" => ""
"keywords" => array:3 [
0 => "U-statistics"
1 => "Functional limit theorems"
2 => "Contractions"
]
"updatedAt" => "2024-09-09 11:39:11"
"publicationUrl" => "https://doi.org/10.1007/s00440-022-01114-3"
"publicationInfo" => array:3 [
"pages" => "367-399"
"volume" => "184"
"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" => """
We prove a multivariate functional version of de Jong’s CLT (J Multivar Anal 34(2):275–289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants in \n
vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the ‘universality of Wiener chaos’ phenomenon first observed in Nourdin et al. (Ann Probab 38(5):1947–1985, 2010).
"""
"en" => """
We prove a multivariate functional version of de Jong’s CLT (J Multivar Anal 34(2):275–289, 1990) yielding that, given a sequence of vectors of Hoeffding-degenerate U-statistics, the corresponding empirical processes on [0, 1] weakly converge in the Skorohod space as soon as their fourth cumulants in \n
vanish asymptotically and a certain strengthening of the Lindeberg-type condition is verified. As an application, we lift to the functional level the ‘universality of Wiener chaos’ phenomenon first observed in Nourdin et al. (Ann Probab 38(5):1947–1985, 2010).
"""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
7 => Essec\Faculty\Model\Contribution {#2209
#_index: "academ_contributions"
#_id: "15113"
#_source: array:18 [
"id" => "15113"
"slug" => "vector-valued-statistics-of-binomial-processes-berry-esseen-bounds-in-the-convex-distance"
"yearMonth" => "2023-10"
"year" => "2023"
"title" => "Vector-valued statistics of binomial processes: Berry–Esseen bounds in the convex distance"
"description" => "KASPRZAK, M. et PECCATI, G. (2023). Vector-valued statistics of binomial processes: Berry–Esseen bounds in the convex distance. <i>Annals of Applied Probability</i>, 33(5)."
"authors" => array:2 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "Peccati Giovanni"
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.1214/22-AAP1897"
"publicationInfo" => array:3 [
"pages" => null
"volume" => "33"
"number" => "5"
]
"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 discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions, holding in every dimension. Such a finding constitutes a substantial extension of the one-dimensional bounds deduced in Chatterjee (Ann. Probab. 36 (2008) 1584–1610) and Lachièze-Rey and Peccati (Ann. Appl. Probab. 27 (2017) 1992–2031), as well as of the multidimensional bounds for smooth test functions and indicators of rectangles derived, respectively, in Dung (Acta Math. Hungar. 158 (2019) 173–201), and Fang and Koike (Ann. Appl. Probab. 31 (2021) 1660–1686). Our techniques involve the use of Stein’s method, combined with a suitable adaptation of the recursive approach inaugurated by Schulte and Yukich (Electron. J. Probab. 24 (2019) 1–42): this yields rates of converge that have a presumably optimal dependence on the sample size. We develop several applications of a geometric nature, among which is a new collection of multidimensional quantitative limit theorems for the intrinsic volumes associated with coverage processes in Euclidean spaces."
"en" => "We study the discrepancy between the distribution of a vector-valued functional of i.i.d. random elements and that of a Gaussian vector. Our main contribution is an explicit bound on the convex distance between the two distributions, holding in every dimension. Such a finding constitutes a substantial extension of the one-dimensional bounds deduced in Chatterjee (Ann. Probab. 36 (2008) 1584–1610) and Lachièze-Rey and Peccati (Ann. Appl. Probab. 27 (2017) 1992–2031), as well as of the multidimensional bounds for smooth test functions and indicators of rectangles derived, respectively, in Dung (Acta Math. Hungar. 158 (2019) 173–201), and Fang and Koike (Ann. Appl. Probab. 31 (2021) 1660–1686). Our techniques involve the use of Stein’s method, combined with a suitable adaptation of the recursive approach inaugurated by Schulte and Yukich (Electron. J. Probab. 24 (2019) 1–42): this yields rates of converge that have a presumably optimal dependence on the sample size. We develop several applications of a geometric nature, among which is a new collection of multidimensional quantitative limit theorems for the intrinsic volumes associated with coverage processes in Euclidean spaces."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
8 => Essec\Faculty\Model\Contribution {#2210
#_index: "academ_contributions"
#_id: "15114"
#_source: array:18 [
"id" => "15114"
"slug" => "a-fourier-representation-of-kernel-stein-discrepancy-with-application-to-goodness-of-fit-tests-for-measures-on-infinite-dimensional-hilbert-spaces"
"yearMonth" => "2025-02"
"year" => "2025"
"title" => "A Fourier Representation of Kernel Stein Discrepancy with Application to Goodness-of-Fit Tests for Measures on Infinite Dimensional Hilbert Spaces"
"description" => "KASPRZAK, M., WYNNE, G. et DUNCAN, A.B. (2025). A Fourier Representation of Kernel Stein Discrepancy with Application to Goodness-of-Fit Tests for Measures on Infinite Dimensional Hilbert Spaces. <i>Bernoulli: A Journal of Mathematical Statistics and Probability</i>."
"authors" => array:3 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "WYNNE George"
]
2 => array:1 [
"name" => "DUNCAN Andrew B."
]
]
"ouvrage" => ""
"keywords" => []
"updatedAt" => "2024-09-05 01:01:34"
"publicationUrl" => null
"publicationInfo" => array:3 [
"pages" => ""
"volume" => ""
"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" => ""
"en" => ""
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
9 => Essec\Faculty\Model\Contribution {#2211
#_index: "academ_contributions"
#_id: "15167"
#_source: array:18 [
"id" => "15167"
"slug" => "validated-variational-inference-via-practical-posterior-error-bounds"
"yearMonth" => "2020-08"
"year" => "2020"
"title" => "Validated Variational Inference via Practical Posterior Error Bounds"
"description" => "HUGGINS, J.H., KASPRZAK, M., CAMPBELL, T. et BRODERICK, T. (2020). Validated Variational Inference via Practical Posterior Error Bounds. Dans: <i>23rd International Conference on Artificial Intelligence and Statistics (AISTATS)</i>. Palermo: Proceedings of Machine Learning Research."
"authors" => array:4 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "HUGGINS Jonathan H."
]
2 => array:1 [
"name" => "CAMPBELL Trevor"
]
3 => array:1 [
"name" => "BRODERICK Tamara"
]
]
"ouvrage" => "23rd International Conference on Artificial Intelligence and Statistics (AISTATS)"
"keywords" => []
"updatedAt" => "2024-09-16 10:16:10"
"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, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
10 => Essec\Faculty\Model\Contribution {#2212
#_index: "academ_contributions"
#_id: "15168"
#_source: array:18 [
"id" => "15168"
"slug" => "a-targeted-accuracy-diagnostic-for-variational-approximations"
"yearMonth" => "2023-04"
"year" => "2023"
"title" => "A Targeted Accuracy Diagnostic for Variational Approximations"
"description" => "WANG, Y., KASPRZAK, M. et HUGGINS, J.H. (2023). A Targeted Accuracy Diagnostic for Variational Approximations. Dans: <i>26th International Conference on Artificial Intelligence and Statistics (AISTATS)</i>. Valencia: Proceedings of Machine Learning Research."
"authors" => array:3 [
0 => array:3 [
"name" => "KASPRZAK Mikolaj"
"bid" => "B00820408"
"slug" => "kasprzak-mikolaj"
]
1 => array:1 [
"name" => "WANG Yu"
]
2 => array:1 [
"name" => "HUGGINS Jonathan H."
]
]
"ouvrage" => "26th International Conference on Artificial Intelligence and Statistics (AISTATS)"
"keywords" => array:2 [
0 => "Variational Inference (VI)"
1 => "accuracy"
]
"updatedAt" => "2024-10-31 13:51:19"
"publicationUrl" => "https://doi.org/10.48550/arXiv.2302.12419"
"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" => "Variational Inference (VI) is an attractive alternative to Markov Chain Monte Carlo (MCMC) due to its computational efficiency in the case of large datasets and/or complex models with high-dimensional parameters. However, evaluating the accuracy of variational approximations remains a challenge. Existing methods characterize the quality of the whole variational distribution, which is almost always poor in realistic applications, even if specific posterior functionals such as the component-wise means or variances are accurate. Hence, these diagnostics are of practical value only in limited circumstances. To address this issue, we propose the TArgeted Diagnostic for Distribution Approximation Accuracy (TADDAA), which uses many short parallel MCMC chains to obtain lower bounds on the error of each posterior functional of interest. We also develop a reliability check for TADDAA to determine when the lower bounds should not be trusted. Numerical experiments validate the practical utility and computational efficiency of our approach on a range of synthetic distributions and real-data examples, including sparse logistic regression and Bayesian neural network models."
"en" => "Variational Inference (VI) is an attractive alternative to Markov Chain Monte Carlo (MCMC) due to its computational efficiency in the case of large datasets and/or complex models with high-dimensional parameters. However, evaluating the accuracy of variational approximations remains a challenge. Existing methods characterize the quality of the whole variational distribution, which is almost always poor in realistic applications, even if specific posterior functionals such as the component-wise means or variances are accurate. Hence, these diagnostics are of practical value only in limited circumstances. To address this issue, we propose the TArgeted Diagnostic for Distribution Approximation Accuracy (TADDAA), which uses many short parallel MCMC chains to obtain lower bounds on the error of each posterior functional of interest. We also develop a reliability check for TADDAA to determine when the lower bounds should not be trusted. Numerical experiments validate the practical utility and computational efficiency of our approach on a range of synthetic distributions and real-data examples, including sparse logistic regression and Bayesian neural network models."
]
"authors_fields" => array:2 [
"fr" => "Systèmes d'Information, Data Analytics et Opérations"
"en" => "Information Systems, Data Analytics and Operations"
]
"indexedAt" => "2024-11-05T00:21:41.000Z"
]
+lang: "en"
+"_type": "_doc"
+"_score": 6.780409
+"parent": null
}
]
"avatar" => "https://faculty.essec.edu/wp-content/uploads/avatars/B00820408.jpg"
"contributionCounts" => 11
"personalLinks" => array:2 [
0 => "<a href="https://orcid.org/0000-0003-0825-7751" target="_blank">ORCID</a>"
1 => "<a href="https://scholar.google.com/citations?user=dcVFn08AAAAJ&hl=en&authuser=1" target="_blank">Google scholar</a>"
]
"docTitle" => "Mikolaj KASPRZAK"
"docSubtitle" => "Assistant Professor"
"docDescription" => "Department: Information Systems, Data Analytics and Operations<br>Campus de Cergy"
"docType" => "cv"
"docPreview" => "<img src="https://faculty.essec.edu/wp-content/uploads/avatars/B00820408.jpg"><span><span>Mikolaj KASPRZAK</span><span>B00820408</span></span>"
"academ_cv_info" => ""
]
#_index: "academ_cv"
+lang: "en"
+"_type": "_doc"
+"_score": 5.0369525
+"parent": null
}