Author: "MOdel for Data Analysis and Learning (MODAL)" / Publication Year Range: Last 3 years - Searchworks@Jio Institute Digital Library Search Results

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68 results on '"MOdel for Data Analysis and Learning (MODAL)"'

1. Effects of Immunoglobulins G From Systemic Sclerosis Patients in Normal Dermal Fibroblasts: A Multi-Omics Study

Author: Aurélien Chepy, Solange Vivier, Fabrice Bray, Camille Ternynck, Jean-Pascal Meneboo, Martin Figeac, Alexandre Filiot, Lucile Guilbert, Manel Jendoubi, Christian Rolando, David Launay, Sylvain Dubucquoi, Guillemette Marot, Vincent Sobanski, Service de médecine interne [Lille], Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Institute for Translational Research in Inflammation - U 1286 (INFINITE (Ex-Liric)), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Lille Inflammation Research International Center - U 995 (LIRIC), Institut Pasteur de Lille, Réseau International des Instituts Pasteur (RIIP)-Réseau International des Instituts Pasteur (RIIP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Miniaturisation pour la Synthèse, l’Analyse et la Protéomique - UAR 3290 (MSAP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Plateformes Lilloises en Biologie et Santé - UAR 2014 - US 41 (PLBS), Réseau International des Instituts Pasteur (RIIP)-Réseau International des Instituts Pasteur (RIIP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Centre National de la Recherche Scientifique (CNRS), Institut d'Immunologie [CHRU Lille], Pôle de Biologie Pathologie Génétique [CHU Lille], Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Université de Lille, CHU Lille, Institute for Translational Research in Inflammation - U 1286 [INFINITE (Ex-Liric)], Institut de Recherche Translationnelle sur l'Inflammation (INFINITE) - U1286, Miniaturisation pour la Synthèse, l'Analyse et la Protéomique (MSAP) - USR 3290, Evaluation des technologies de santé et des pratiques médicales - ULR 2694 [METRICS], Plateformes Lilloises en Biologie et Santé - UAR 2014 - US 41 [PLBS], Miniaturisation pour la Synthèse, l’Analyse et la Protéomique - UAR 3290 [MSAP], MOdel for Data Analysis and Learning [MODAL], METRICS : Evaluation des technologies de santé et des pratiques médicales - ULR 2694, and Institut Universitaire de France [IUF]
Subjects: systemic sclerosis, multi-omics analysis, autoantibodies, proteomics, transcriptomics, Scleroderma, Systemic, Proteome, [SDV]Life Sciences [q-bio], Immunology, Fibroblasts, Tandem Mass Spectrometry, Immunoglobulin G, Humans, Immunology and Allergy, Chromatography, Liquid
Abstract: International audience; Autoantibodies (Aabs) are frequent in systemic sclerosis (SSc). Although recognized as potent biomarkers, their pathogenic role is debated. This study explored the effect of purified immunoglobulin G (IgG) from SSc patients on protein and mRNA expression of dermal fibroblasts (FBs) using an innovative multi-omics approach. Dermal FBs were cultured in the presence of sera or purified IgG from patients with diffuse cutaneous SSc (dcSSc), limited cutaneous SSc or healthy controls (HCs). The FB proteome and transcriptome were explored using liquid chromatography coupled with tandem mass spectrometry (LC-MS/MS) and microarray assays, respectively. Proteomic analysis identified 3,310 proteins. SSc sera and purified IgG induced singular protein profile patterns. These FB proteome changes depended on the Aab serotype, with a singular effect observed with purified IgG from anti-topoisomerase-I autoantibody (ATA) positive patients compared to HC or other SSc serotypes. IgG from ATA positive SSc patients induced enrichment in proteins involved in focal adhesion, cadherin binding, cytosolic part, or lytic vacuole. Multi-omics analysis was performed in two ways: first by restricting the analysis of the transcriptomic data to differentially expressed proteins; and secondly, by performing a global statistical analysis integrating proteomics and transcriptomics. Transcriptomic analysis distinguished 764 differentially expressed genes and revealed that IgG from dcSSc can induce extracellular matrix (ECM) remodeling changes in gene expression profiles in FB. Global statistical analysis integrating proteomics and transcriptomics confirmed that IgG from SSc can induce ECM remodeling and activate FB profiles. This effect depended on the serotype of the patient, suggesting that SSc Aab might play a pathogenic role in some SSc subsets.
Published: 2022

2. MMD-FUSE: Learning and Combining Kernels for Two-Sample Testing Without Data Splitting

Author: Biggs, Felix, Schrab, Antonin, Gretton, Arthur, University College of London [London] (UCL), Gatsby Computational Neuroscience Unit, Department of Computer science [University College of London] (UCL-CS), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: Methodology (stat.ME), FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, FOS: Mathematics, Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), Statistics - Methodology, Machine Learning (cs.LG)
Abstract: We propose novel statistics which maximise the power of a two-sample test based on the Maximum Mean Discrepancy (MMD), by adapting over the set of kernels used in defining it. For finite sets, this reduces to combining (normalised) MMD values under each of these kernels via a weighted soft maximum. Exponential concentration bounds are proved for our proposed statistics under the null and alternative. We further show how these kernels can be chosen in a data-dependent but permutation-independent way, in a well-calibrated test, avoiding data splitting. This technique applies more broadly to general permutation-based MMD testing, and includes the use of deep kernels with features learnt using unsupervised models such as auto-encoders. We highlight the applicability of our MMD-FUSE test on both synthetic low-dimensional and real-world high-dimensional data, and compare its performance in terms of power against current state-of-the-art kernel tests., 42 pages, 7 figures, 1 table
Published: 2023

3. Learning via Wasserstein-Based High Probability Generalisation Bounds

Author: Viallard, Paul, Haddouche, Maxime, Şimşekli, Umut, Guedj, Benjamin, Statistical Machine Learning and Parsimony (SIERRA), Département d'informatique - ENS Paris (DI-ENS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), The Inria London Programme (Inria-London), Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), University College of London [London] (UCL), Grant number EP/R013616/1, ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), ANR-18-CE40-0016,BEAGLE,Apprentissage PAC-bayésien agnostique(2018), ANR-18-CE23-0015,APRIORI,Une Perspective PAC-Bayésienne de l'Apprentissage de Représentations(2018), and European Project: 101039676,DYNASTY
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Machine Learning (stat.ML), Machine Learning (cs.LG)
Abstract: Minimising upper bounds on the population risk or the generalisation gap has been widely used in structural risk minimisation (SRM) - this is in particular at the core of PAC-Bayesian learning. Despite its successes and unfailing surge of interest in recent years, a limitation of the PAC-Bayesian framework is that most bounds involve a Kullback-Leibler (KL) divergence term (or its variations), which might exhibit erratic behavior and fail to capture the underlying geometric structure of the learning problem - hence restricting its use in practical applications. As a remedy, recent studies have attempted to replace the KL divergence in the PAC-Bayesian bounds with the Wasserstein distance. Even though these bounds alleviated the aforementioned issues to a certain extent, they either hold in expectation, are for bounded losses, or are nontrivial to minimize in an SRM framework. In this work, we contribute to this line of research and prove novel Wasserstein distance-based PAC-Bayesian generalisation bounds for both batch learning with independent and identically distributed (i.i.d.) data, and online learning with potentially non-i.i.d. data. Contrary to previous art, our bounds are stronger in the sense that (i) they hold with high probability, (ii) they apply to unbounded (potentially heavy-tailed) losses, and (iii) they lead to optimizable training objectives that can be used in SRM. As a result we derive novel Wasserstein-based PAC-Bayesian learning algorithms and we illustrate their empirical advantage on a variety of experiments.
Published: 2023

4. MLGL: An R Package Implementing Correlated Variable Selection by Hierarchical Clustering and Group-Lasso

Author: Grimonprez, Quentin, Blanck, Samuel, Celisse, Alain, Marot, Guillemette, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne) (SAMM), Université Paris 1 Panthéon-Sorbonne (UP1), We thank Direction Générale de l’Armement (DGA) and Inria for a financial support of Quentin Grimonprez’s PhD, and the CPER Nord-Pas de Calais/FEDER DATA Advanced data science and technologies 2015-2020., Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), and Marot, Guillemette
Subjects: Mathematical statistics, group selection, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], correlated variables, penalized regression, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], hierarchical clustering
Abstract: International audience; The MLGL R-package, standing for Multi-Layer Group-Lasso, implements a new procedure of variable selection in the context of redundancy between explanatory variables, which holds true with high dimensional data. A sparsity assumption is made that is, only a few variables are assumed to be relevant for predicting the response variable. In this context, the performance of classical Lasso-based approaches strongly deteriorates as the redundancy strengthens. The proposed approach combines variables aggregation and selection in order to improve interpretability and performance. First, a hierarchical clustering procedure provides at each level a partition of the variables into groups. Then, the set of groups of variables from the different levels of the hierarchy is given as input to group-Lasso, with weights adapted to the structure of the hierarchy. At this step, group-Lasso outputs sets of candidate groups of variables for each value of regularization parameter. The versatility offered by MLGL to choose groups at different levels of the hierarchy a priori induces a high computational complexity. MLGL however exploits the structure of the hierarchy and the weights used in group-Lasso to greatly reduce the final time cost. The final choice of the regularization parameter – and therefore the final choice of groups – is made by a multiple hierarchical testing procedure.
Published: 2023

5. Optimistic Dynamic Regret Bounds

Author: Haddouche, Maxime, Guedj, Benjamin, Wintenberger, Olivier, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, Machine Learning (stat.ML), Mathematics - Optimization and Control, Machine Learning (cs.LG)
Abstract: Online Learning (OL) algorithms have originally been developed to guarantee good performances when comparing their output to the best fixed strategy. The question of performance with respect to dynamic strategies remains an active research topic. We develop in this work dynamic adaptations of classical OL algorithms based on the use of experts' advice and the notion of optimism. We also propose a constructivist method to generate those advices and eventually provide both theoretical and experimental guarantees for our procedures.
Published: 2023

6. Impact of Missing Data on Mixtures and Clustering

Author: Biernacki, Christophe, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Biernacki, Christophe
Subjects: [STAT]Statistics [stat], [STAT] Statistics [stat]
Abstract: International audience
Published: 2022

7. The Patient Path: a first approach

Author: Essifi, Rim, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Équipe MODAL, Projet PATH, and Essifi, Rim
Subjects: care pathways, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], longitudinal data analysis, Gaussian processes, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], functional data analysis, clustering
Abstract: International audience; European healthcare systems are faced with multiple challenges, including anaging population, an increase in chronic diseases and patients withmulti-morbidity, and limited financial and human resources. The response tothese challenges is based in particular on the organisation of care into carepathways. Namely, Once the data necessary for the construction of a carepathway are acquired and processed, one has to model the patient pathwaymathematically in a generic way. After that, using clustering algorithms, one canidentify patients subgroups, then, mine for common treatments, predict thefuture of patient pathways and answer clinicians’ questions. All these steps wouldlead to an automated processes which has to be evaluated by medical experts.Available statistical methods remain limited and inefficient to construct carepathways. Indeed, data obtained from health care providers and insurancecompanies are all time-dependent, highly heterogeneous, qualitative in part, withseveral thousand possible modalities and mainly made up of missing data. Wepropose an approach based on functional data analysis combined withlongitudinal data analysis in order to construct care pathways.
Published: 2022

8. Efficient iterative methods for clustering and matching problems on graphs

Author: Braun, Guillaume, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Université de Lille, Christophe Biernacki, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), and Hemant Tyagi (co-encadrant)
Subjects: SBM, classification, Graph clustering, Power method, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-CO]Mathematics [math]/Combinatorics [math.CO], iterative methods, méthodes itératives, Graph matching, Alignement de graphes, Modèle à blocs stochastiques, clustering, Méthode de la puissance généralisée
Abstract: Graph structured datasets arise naturally in many fields including biology with protein-to-protein interaction networks, ecology with predator-prey networks and economy with financial market networks. In order to extract relevant information from these networks, one often uses clustering methods to gather nodes having similar connectivity patterns into communities. Numerous clustering algorithms have been proposed in the past decade and have been analyzed under the Stochastic Block Model (SBM), a popular random graph model. However, in practice, one often has access to side information, and it is typically unclear how this information can be incorporated in existing methods and to what extent it can help to improve the clustering performance.We will first address this question under the Contextual SBM (CSBM) -- a simple extension of the SBM with independent Gaussian covariates associated to each nodes -- and propose an iterative refinement method that is fast and achieves the information theoretic threshold for exact recovery. Our method is inspired by the Generalized Power Method (GPM) and principles of EM type algorithms.Next, we extend the method in order to be applied to networks with heterogeneous degrees or mixed-membership, but also with different kind of covariates like multilayer graphs with possibly missing values, or high dimensional bipartite graphs, hence showing the flexibility of the approach.Lastly, we consider the graph matching problem where the additional graphs can be considered as correlated side information. We show that we can also use the GPM for this problem to significantly improve the matching obtained by state-of-the art methods, and provide consistency guarantees for the GPM under the Correlated Wigner Model (CoWM).; Des données structurées sous forme de graphe apparaissent naturellement dans de nombreux domaines comme la biologie avec les réseaux d'interaction protéine-protéine, l'écologie avec les réseaux proie-prédateur ou l'économie avec les réseaux financiers. Afin d'extraire une information pertinente de ces réseaux, on a souvent recours à des méthodes de classification qui regroupent entre eux les nœuds ayant un profil de connectivité similaire. Durant les vingt dernières années, de nombreux algorithmes de classification ont été proposés et analysés lorsque le graphe est généré par un modèle à blocs stochastiques (SBM). Mais en pratique, on a souvent accès à de l'information auxiliaire. Il n'est toutefois pas bien compris comment cette information auxiliaire peut-être incorporée par les méthodes existantes, et dans quelle mesure elle peut aider à améliorer les résultats de la classification.Dans un premier temps nous allons résoudre ce problème en s'appuyant sur un modèle génératif simple - le modèle à blocs stochastiques contextuel (CSBM) - qui ajoute à chaque nœud d'un graphe généré par un SBM des covariables gaussiennes. Nous proposons une méthode itérative rapide qui atteint le seuil théorique d'information pour le recouvrement exact des communautés latentes. Notre méthode s'inspire de la méthode de la puissance généralisée (GPM) ainsi que des algorithmes de type EM.Nous étendons ensuite la méthode à des graphes ayant des nœuds avec des degrés hétérogènes ou appartenant à plusieurs communautés, ainsi qu'à des covariables de différentes natures, comme par exemple des réseaux multicouches avec des valeurs manquantes ou des graphes bipartites en grande dimension.Enfin, nous considérons le problème d'appariement de graphes dans lequel le graphe additionnel peut être considéré comme de l'information auxiliaire corrélée. Nous montrons que l'on peut également utiliser une stratégie basée sur GPM pour améliorer de manière significative un appariement initial imparfait. Nous établissons des garanties de consistance de l'algorithme sous le modèle de Wigner corrélé (CoWM).
Published: 2022

9. Contribution à la statistique spatiale for données de grande dimension et de survie

Author: Frévent, Camille, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Université de Lille, Michaël Genin, and Sophie Dabo-Niang
Subjects: Statistique spatiale, High-dimensional data, Survival data, Spatial statistic, Supervised analysis, Données de survie, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Unsupervised analysis, Données en grande dimension, Clusters detection, Analyse non supervisée, Analyse supervisée, Détection de clusters
Abstract: In this thesis, we are interested in statistical spatial learning for high-dimensional and survival data. The objective is to develop unsupervised cluster detection methods by means of spatial scan statistics in the contexts of functional data analysis in one hand and survival data analysis in the other hand. In the first two chapters, we consider univariate and multivariate functional data measured spatially in a geographical area. We propose both parametric and nonparametric spatial scan statistics in this framework. These univariate and multivariate functional approaches avoid the loss of information respectively of a univariate method or a multivariate method applied on the average of the observations during the study period. We study the new methods' performances in simulation studies before applying them on economic and environmental real data. We are also interested in spatial cluster detection of survival data. Although there exist already spatial scan statistics approaches in this framework in the literature, these do not take into account a potential correlation of survival times between individuals of the same spatial unit. Moreover, the spatial nature of the data implies a potential correlation between the spatial units, which should be taken into account. The originality of our proposed method is to introduce a spatial scan statistic based on a Cox model with a spatial frailty, allowing to take into account both the potential correlation between the individuals of the same spatial unit and the potential correlation between the spatial units.We compare the performances of this new approach with the existing methods and apply them on real data corresponding to survival times of elderly people with end-stage kidney failure in northern France. Finally, we propose a number of perspectives to our work, both in a direct extension of this thesis in the framework of spatial scan statistics for high-dimensional and survival data, but also perspectives in a broader context of unsupervised spatial analysis (spatial clustering for high-dimensional data (tensors)), and supervised spatial learning (regression); Dans ce mémoire de thèse nous nous intéressons aux méthodes d'apprentissage statistique pour données spatiales en grande dimension et données de survie. L'objectif est de développer des méthodes de détection de clusters non supervisées avec des statistiques de scan spatiales, à la fois dans le cadre de l'analyse de données fonctionnelles, mais aussi pour l'analyse de données de survie. Nous considérons tout d'abord des données fonctionnelles univariées ou multivariées mesurées spatialement dans une région géographique. Nous proposons des statistiques de scan paramétriques et non paramétriques dans ce contexte. Ces approches fonctionnelles univariées et multivariées évitent la perte d'information respectivement d'une méthode univariée ou multivariée appliquée sur des observations moyennes au cours de la période d'étude. Nous étudions également les performances de ces approches sur des études de simulation, avant de les appliquer sur des données réelles économiques et environnementales. Nous nous intéressons également à la détection de clusters spatiaux de temps de survie. Bien qu'il existe déjà dans la littérature des approches de statistiques de scan spatiale dans ce cadre, celles-ci ne permettent pas de prendre en compte une éventuelle corrélation entre les individus d'une même unité spatiale. De plus, la nature spatiale des données implique une potentielle corrélation entre les unités spatiales, qui doit être prise en compte. L'originalité de l'approche que nous proposons est le développement d'une nouvelle statistique de scan spatiale basée sur un modèle de Cox à fragilité spatiale, permettant à la fois la prise en compte de la corrélation entre les individus d'une même unité spatiale, et une éventuelle corrélation entre les unités spatiales. Nous avons comparé les performances de cette nouvelle approche avec les méthodes existantes et nous les avons appliquées sur des données réelles de temps de survie des personnes âgées atteintes d'insuffisance rénale chronique terminale dans le nord de la France. Enfin, nous proposons un certain nombre de perspectives à notre travail, à la fois avec des prolongements directs à cette thèse dans le cadre des statistiques de scan spatiales pour données en grande dimension et données de survie, mais également avec des perspectives dans un cadre plus large d'analyse spatiale non supervisée (clustering spatial pour données en grande dimension modélisées par des tenseurs), et d'apprentissage spatial supervisé (régression).
Published: 2022

10. Minimax Optimal Clustering of Bipartite Graphs with a Generalized Power Method

Author: Braun, Guillaume, Tyagi, Hemant, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Tyagi, Hemant
Subjects: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Mathematics - Statistics Theory, Statistics Theory (math.ST), [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Abstract: Clustering bipartite graphs is a fundamental task in network analysis. In the high-dimensional regime where the number of rows $n_1$ and the number of columns $n_2$ of the associated adjacency matrix are of different order, existing methods derived from the ones used for symmetric graphs can come with sub-optimal guarantees. Due to increasing number of applications for bipartite graphs in the high dimensional regime, it is of fundamental importance to design optimal algorithms for this setting. The recent work of Ndaoud et al. (2022) improves the existing upper-bound for the misclustering rate in the special case where the columns (resp. rows) can be partitioned into $L = 2$ (resp. $K = 2$) communities. Unfortunately, their algorithm cannot be extended to the more general setting where $K \neq L \geq 2$. We overcome this limitation by introducing a new algorithm based on the power method. We derive conditions for exact recovery in the general setting where $K \neq L \geq 2$, and show that it recovers the result in Ndaoud et al. (2022). We also derive a minimax lower bound on the misclustering error when $K = L$ under a symmetric version of our model, which matches the corresponding upper bound up to a factor depending on $K$., Corrections of minor typos and extension of the minimax lower bound to the more general case where $K=L\geq 2$
Published: 2022

11. Seeded graph matching for the correlated Wigner model via the projected power method

Author: Araya, Ernesto, Braun, Guillaume, Tyagi, Hemant, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Tyagi, Hemant
Subjects: Statistics - Machine Learning, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Mathematics - Statistics Theory, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Abstract: In the graph matching problem we observe two graphs $G,H$ and the goal is to find an assignment (or matching) between their vertices such that some measure of edge agreement is maximized. We assume in this work that the observed pair $G,H$ has been drawn from the correlated Wigner model -- a popular model for correlated weighted graphs -- where the entries of the adjacency matrices of $G$ and $H$ are independent Gaussians and each edge of $G$ is correlated with one edge of $H$ (determined by the unknown matching) with the edge correlation described by a parameter $\sigma\in [0,1)$. In this paper, we analyse the performance of the projected power method (PPM) as a seeded graph matching algorithm where we are given an initial partially correct matching (called the seed) as side information. We prove that if the seed is close enough to the ground-truth matching, then with high probability, PPM iteratively improves the seed and recovers the ground-truth matching (either partially or exactly) in $\mathcal{O}(\log n)$ iterations. Our results prove that PPM works even in regimes of constant $\sigma$, thus extending the analysis in (Mao et al.,2021) for the sparse Erd\"os-Renyi model to the (dense) Wigner model. As a byproduct of our analysis, we see that the PPM framework generalizes some of the state-of-art algorithms for seeded graph matching. We support and complement our theoretical findings with numerical experiments on synthetic data.
Published: 2022

12. Dynamic Ranking and Translation Synchronization

Author: Araya, Ernesto, Karlé, Eglantine, Tyagi, Hemant, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Tyagi, Hemant
Subjects: FOS: Computer and information sciences, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML]
Abstract: In many applications, such as sport tournaments or recommendation systems, we have at our disposal data consisting of pairwise comparisons between a set of $n$ items (or players). The objective is to use this data to infer the latent strength of each item and/or their ranking. Existing results for this problem predominantly focus on the setting consisting of a single comparison graph $G$. However, there exist scenarios (e.g., sports tournaments) where the the pairwise comparison data evolves with time. Theoretical results for this dynamic setting are relatively limited and is the focus of this paper. We study an extension of the \emph{translation synchronization} problem, to the dynamic setting. In this setup, we are given a sequence of comparison graphs $(G_t)_{t\in \mathcal{T}}$, where $\mathcal{T} \subset [0,1]$ is a grid representing the time domain, and for each item $i$ and time $t\in \mathcal{T}$ there is an associated unknown strength parameter $z^*_{t,i}\in \mathbb{R}$. We aim to recover, for $t\in\mathcal{T}$, the strength vector $z^*_t=(z^*_{t,1},\dots,z^*_{t,n})$ from noisy measurements of $z^*_{t,i}-z^*_{t,j}$, where $\{i,j\}$ is an edge in $G_t$. Assuming that $z^*_t$ evolves smoothly in $t$, we propose two estimators -- one based on a smoothness-penalized least squares approach and the other based on projection onto the low frequency eigenspace of a suitable smoothness operator. For both estimators, we provide finite sample bounds for the $\ell_2$ estimation error under the assumption that $G_t$ is connected for all $t\in \mathcal{T}$, thus proving the consistency of the proposed methods in terms of the grid size $|\mathcal{T}|$. We complement our theoretical findings with experiments on synthetic and real data., Comment: 39 pages, 8 figures, 2 tables, corrected minor typos; edit after revision; accepted in Inference and Inference, a journal of IMA
Published: 2022

13. The R Package \pkg{HDSpatialScan} for the Detection of Clusters of Multivariate and Functional Data using Spatial Scan Statistics

Author: Frévent, Camille, Ahmed, Mohamed-Salem, Soula, Julien, Smida, Zaineb, Cucala, Lionel, Dabo-Niang, Sophie, Genin, Michaël, Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Dabo-Niang, Sophie
Subjects: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Published: 2022

14. Asymptotic properties of nonparametric quantile estimation with spatial dependency

Author: S.‐H. Arnaud Kanga, Ouagnina Hili, Sophie Dabo‐Niang, Assi N'Guessan, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: Statistics and Probability, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Probability and Uncertainty
Abstract: International audience
Published: 2022

15. Spatial Relative Risk of Upper Aerodigestive Tract Cancers Incidence in French Northern Region

Author: Sophie Dabo-Niang, Emad Darwich, Leila Hamdad, Baba Thiam, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: Computational Theory and Mathematics, General Computer Science, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Computer Networks and Communications, Artificial Intelligence, Computer Graphics and Computer-Aided Design, Computer Science Applications
Abstract: International audience
Published: 2022

16. Tighter PAC-Bayes Generalisation Bounds by Leveraging Example Difficulty

Author: Biggs, Felix, Guedj, Benjamin, Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Machine Learning (stat.ML), Machine Learning (cs.LG)
Abstract: We introduce a modified version of the excess risk, which can be used to obtain tighter, fast-rate PAC-Bayesian generalisation bounds. This modified excess risk leverages information about the relative hardness of data examples to reduce the variance of its empirical counterpart, tightening the bound. We combine this with a new bound for $[-1, 1]$-valued (and potentially non-independent) signed losses, which is more favourable when they empirically have low variance around $0$. The primary new technical tool is a novel result for sequences of interdependent random vectors which may be of independent interest. We empirically evaluate these new bounds on a number of real-world datasets., 22 pages
Published: 2022

17. A PAC-Bayes bound for deterministic classifiers

Author: Clerico, Eugenio, Deligiannidis, George, Guedj, Benjamin, Doucet, Arnaud, University of Oxford, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH]
Abstract: We establish a disintegrated PAC-Bayesian bound, for classifiers that are trained via continuous-time (non-stochastic) gradient descent. Contrarily to what is standard in the PAC-Bayesian setting, our result applies to a training algorithm that is deterministic, conditioned on a random initialisation, without requiring any $\textit{de-randomisation}$ step. We provide a broad discussion of the main features of the bound that we propose, and we study analytically and empirically its behaviour on linear models, finding promising results.
Published: 2022

18. PAC-Bayes with Unbounded Losses through Supermartingales

Author: Haddouche, Maxime, Guedj, Benjamin, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), University College of London [London] (UCL), Computer science department [University College London] (UCL-CS), The Alan Turing Institute, The Inria London Programme (Inria-London), and University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], generalisation bounds, unbounded losses, PAC-Bayes, [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], supermartingales
Abstract: While PAC-Bayes is now an established learning framework for bounded losses, its extension to the case of unbounded losses (as simple as the squared loss on an unbounded space) remains largely uncharted and has attracted a growing interest in recent years. We contribute to this line of work by developing an extention of Markov's inequality for supermartingales, which we use to establish a novel PAC-Bayesian generalisation bound holding for unbounded losses. We show that this bound extends, unifies and even improves on existing PAC-Bayesian bounds.
Published: 2022

19. An extension of the angular synchronization problem to the heterogeneous setting

Author: Cucuringu, M, Tyagi, H, Department of Statistics [Oxford], University of Oxford [Oxford], MOdel for Data Analysis and Learning (MODAL), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, University of Oxford, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, group synchronization, Computer Science - Information Theory, Information Theory (cs.IT), singular value decomposition, Machine Learning (stat.ML), Numerical Analysis (math.NA), random matrix theory, Machine Learning (cs.LG), Statistics - Machine Learning, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], FOS: Mathematics, Mathematics - Numerical Analysis, spectral algorithms, matrix perturbation theory
Abstract: Given an undirected measurement graph $G = ([n], E)$, the classical angular synchronization problem consists of recovering unknown angles $\theta_1,\dots,\theta_n$ from a collection of noisy pairwise measurements of the form $(\theta_i - \theta_j) \mod 2\pi$, for each $\{i,j\} \in E$. This problem arises in a variety of applications, including computer vision, time synchronization of distributed networks, and ranking from preference relationships. In this paper, we consider a generalization to the setting where there exist $k$ unknown groups of angles $\theta_{l,1}, \dots,\theta_{l,n}$, for $l=1,\dots,k$. For each $ \{i,j\} \in E$, we are given noisy pairwise measurements of the form $\theta_{\ell,i} - \theta_{\ell,j}$ for an unknown $\ell \in \{1,2,\ldots,k\}$. This can be thought of as a natural extension of the angular synchronization problem to the heterogeneous setting of multiple groups of angles, where the measurement graph has an unknown edge-disjoint decomposition $G = G_1 \cup G_2 \ldots \cup G_k$, where the $G_i$'s denote the subgraphs of edges corresponding to each group. We propose a probabilistic generative model for this problem, along with a spectral algorithm for which we provide a detailed theoretical analysis in terms of robustness against both sampling sparsity and noise. The theoretical findings are complemented by a comprehensive set of numerical experiments, showcasing the efficacy of our algorithm under various parameter regimes. Finally, we consider an application of bi-synchronization to the graph realization problem, and provide along the way an iterative graph disentangling procedure that uncovers the subgraphs $G_i$, $i=1,\ldots,k$ which is of independent interest, as it is shown to improve the final recovery accuracy across all the experiments considered., Comment: 45 pages, 17 figures
Published: 2022

20. A Survey on Model-Based Co-Clustering: High Dimension and Estimation Challenges

Author: Biernacki, Christophe, Jacques, Julien, Keribin, C., MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Université de Lyon, Statistique mathématique et apprentissage (CELESTE), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Biernacki, Christophe
Subjects: model selection, [STAT.ME] Statistics [stat]/Methodology [stat.ME], High dimension clustering, EM-like algorithms, mixture models, mixed data types, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract: Model-based co-clustering can be seen as a particularly valuable extension of model-based clustering for three main reasons: (1) while allowing parsimoniously a drastic reduction of both the number of lines/individuals and columns/variables of a data set, (2) it also allows interpretability of such a resulting reduced data set since initial individuals and features meaning is preserved in this latter; (3) moreover it benefits from the powerful mathematical statistics theory for both estimation and model selection. Hence, many authors produced new advances on this topic in the recent years, and this paper offers a general update of the related literature. In addition, it is the opportunity to pass two messages, supported by specific research materials: (1) co-clustering still requires some new and motivating researches for fixing some well-identified estimation issues, (2) co-clustering is probably one of the most promising clustering approach to be addressed in the (very) high dimension setting, which corresponds to the global trend on modern data sets
Published: 2022

21. MMD Aggregated Two-Sample Test

Author: Schrab, Antonin, Kim, Ilmun, Albert, Mélisande, Laurent, Béatrice, Guedj, Benjamin, Gretton, Arthur, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), The Inria London Programme (Inria-London), Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), University College of London [London] (UCL), Yonsei University, Institut de Mathématiques de Toulouse UMR5219 (IMT), Université Toulouse Capitole (UT Capitole), Université de Toulouse (UT)-Université de Toulouse (UT)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J), Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3), Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), Gatsby Computational Neuroscience Unit, Partial support from the French National Agency for Research, grants ANR-18-CE40-0016-01 and ANR-18-CE23-0015-02, ANR-19-P3IA-0004,ANITI,Artificial and Natural Intelligence Toulouse Institute(2019), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Computer science department [University College London] (UCL-CS), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3), Université Fédérale Toulouse Midi-Pyrénées-Centre National de la Recherche Scientifique (CNRS), Institut National des Sciences Appliquées (INSA), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université Toulouse 1 Capitole (UT1), Université Fédérale Toulouse Midi-Pyrénées-Université Fédérale Toulouse Midi-Pyrénées-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse), and Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Toulouse - Jean Jaurès (UT2J)-Université Toulouse III - Paul Sabatier (UT3)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, Kernel methods, Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Minimax adaptivity, Machine Learning (cs.LG), Methodology (stat.ME), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Two-sample testing, FOS: Mathematics, Statistics - Methodology
Abstract: We propose two novel nonparametric two-sample kernel tests based on the Maximum Mean Discrepancy (MMD). First, for a fixed kernel, we construct an MMD test using either permutations or a wild bootstrap, two popular numerical procedures to determine the test threshold. We prove that this test controls the probability of type I error non-asymptotically. Hence, it can be used reliably even in settings with small sample sizes as it remains well-calibrated, which differs from previous MMD tests which only guarantee correct test level asymptotically. When the difference in densities lies in a Sobolev ball, we prove minimax optimality of our MMD test with a specific kernel depending on the smoothness parameter of the Sobolev ball. In practice, this parameter is unknown and, hence, the optimal MMD test with this particular kernel cannot be used. To overcome this issue, we construct an aggregated test, called MMDAgg, which is adaptive to the smoothness parameter. The test power is maximised over the collection of kernels used, without requiring held-out data for kernel selection (which results in a loss of test power), or arbitrary kernel choices such as the median heuristic. We prove that MMDAgg still controls the level non-asymptotically, and achieves the minimax rate over Sobolev balls, up to an iterated logarithmic term. Our guarantees are not restricted to a specific type of kernel, but hold for any product of one-dimensional translation invariant characteristic kernels. We provide a user-friendly parameter-free implementation of MMDAgg using an adaptive collection of bandwidths. We demonstrate that MMDAgg significantly outperforms alternative state-of-the-art MMD-based two-sample tests on synthetic data satisfying the Sobolev smoothness assumption, and that, on real-world image data, MMDAgg closely matches the power of tests leveraging the use of models such as neural networks., 80 pages
Published: 2022

22. Meta-analysis of RNA-Seq data

Author: Marot, Guillemette, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), PLBS, bilille and GoaL platforms, and Marot, Guillemette
Subjects: [STAT]Statistics [stat], [STAT.AP]Statistics [stat]/Applications [stat.AP], [STAT.AP] Statistics [stat]/Applications [stat.AP], [STAT] Statistics [stat]
Abstract: National audience
Published: 2022

23. Discussion of 'Multiscale Fisher's Independence Test for Multivariate Dependence'

Author: Antonin Schrab, Wittawat Jitkrittum, Zoltán Szabó, Dino Sejdinovic, Arthur Gretton, Schrab, Antonin, Gatsby Computational Neuroscience Unit, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.ME] Statistics [stat]/Methodology [stat.ME], [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Machine Learning (stat.ML), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Statistics - Applications, Statistics - Computation, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), Methodology (stat.ME), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, Applications (stat.AP), [STAT.ME]Statistics [stat]/Methodology [stat.ME], Computation (stat.CO), Statistics - Methodology
Abstract: We discuss how MultiFIT, the Multiscale Fisher's Independence Test for Multivariate Dependence proposed by Gorsky and Ma (2022), compares to existing linear-time kernel tests based on the Hilbert-Schmidt independence criterion (HSIC). We highlight the fact that the levels of the kernel tests at any finite sample size can be controlled exactly, as it is the case with the level of MultiFIT. In our experiments, we observe some of the performance limitations of MultiFIT in terms of test power., 8 pages
Published: 2022

24. Efficient Aggregated Kernel Tests using Incomplete $U$-statistics

Author: Antonin Schrab, Ilmun Kim, Benjamin Guedj, Arthur Gretton, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Guedj, Benjamin
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), Methodology (stat.ME), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, FOS: Mathematics, Statistics - Methodology
Abstract: We propose a series of computationally efficient nonparametric tests for the two-sample, independence, and goodness-of-fit problems, using the Maximum Mean Discrepancy (MMD), Hilbert Schmidt Independence Criterion (HSIC), and Kernel Stein Discrepancy (KSD), respectively. Our test statistics are incomplete $U$-statistics, with a computational cost that interpolates between linear time in the number of samples, and quadratic time, as associated with classical $U$-statistic tests. The three proposed tests aggregate over several kernel bandwidths to detect departures from the null on various scales: we call the resulting tests MMDAggInc, HSICAggInc and KSDAggInc. This procedure provides a solution to the fundamental kernel selection problem as we can aggregate a large number of kernels with several bandwidths without incurring a significant loss of test power. For the test thresholds, we derive a quantile bound for wild bootstrapped incomplete $U$-statistics, which is of independent interest. We derive non-asymptotic uniform separation rates for MMDAggInc and HSICAggInc, and quantify exactly the trade-off between computational efficiency and the attainable rates: this result is novel for tests based on incomplete $U$-statistics, to our knowledge. We further show that in the quadratic-time case, the wild bootstrap incurs no penalty to test power over the more widespread permutation-based approach, since both attain the same minimax optimal rates (which in turn match the rates that use oracle quantiles). We support our claims with numerical experiments on the trade-off between computational efficiency and test power. In all three testing frameworks, the linear-time versions of our proposed tests perform at least as well as the current linear-time state-of-the-art tests., 34 pages, 5 figures
Published: 2022

25. On Margins and Generalisation for Voting Classifiers

Author: Biggs, Felix, Zantedeschi, Valentina, Guedj, Benjamin, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Guedj, Benjamin
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.TH] Statistics [stat]/Statistics Theory [stat.TH], Mathematics - Statistics Theory, Machine Learning (stat.ML), [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), ComputingMethodologies_PATTERNRECOGNITION, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, FOS: Mathematics
Abstract: We study the generalisation properties of majority voting on finite ensembles of classifiers, proving margin-based generalisation bounds via the PAC-Bayes theory. These provide state-of-the-art guarantees on a number of classification tasks. Our central results leverage the Dirichlet posteriors studied recently by Zantedeschi et al. [2021] for training voting classifiers; in contrast to that work our bounds apply to non-randomised votes via the use of margins. Our contributions add perspective to the debate on the "margins theory" proposed by Schapire et al. [1998] for the generalisation of ensemble classifiers., Comment: 20 pages, 8 figures
Published: 2022

26. Variable selection with Multi-Layer Group Lasso

Author: Marot, Guillemette, Grimonprez, Quentin, Blanck, Samuel, Celisse, Alain, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), and Marot, Guillemette
Subjects: [MATH] Mathematics [math], [MATH]Mathematics [math]
Abstract: International audience; The MLGL (Multi-Layer Group-Lasso) R package implements a new procedure of variable selection in the context of redundancy between explanatory variables, which holds true with high0dimensional data. A sparsity assumption is made–that is, only a few variables are assumed to be relevant for predicting the response variable. In this context, the performance of classical Lasso-based approaches strongly deteriorates as the redundancy strengthens.The proposed approach combines variables aggregation and selection in order to improve interpretability and performance. First, a hierarchical clustering procedure provides at each level a partition of the variables into groups. Then, the set of groups of variables from the different levels of the hierarchy is given as input to group-Lasso, with weights adapted to the structure of the hierarchy. At this step, group-Lasso outputs sets of candidate groups of variables for each value of regularization parameter.The versatility offered by MLGL to choose groups at different levels of the hierarchy a priori induces a high computational complexity. MLGL, however, exploits the structure of the hierarchy and the weights used in group-Lasso to greatly reduce the final time cost. The final choice of the regularization parameter–and therefore the final choice of groups–is made by a multiple hierarchical testing procedure.
Published: 2022

27. [Letter to editor] Altered microRNA expression in severe COVID‐19: Potential prognostic and pathophysiological role

Author: Garnier, Nathalie, Pollet, Kato, Fourcot, Marie, Caplan, Morgan, Marot, Guillemette, Goutay, Julien, Labreuche, Julien, Soncin, F., Boukherroub, Rabah, Hober, Didier, Szunerits, Sabine, Poissy, Julien, Engelmann, Ilka, Hospices Civils de Lyon (HCL), Ingénieries santé médicament, Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), CHU Lille, Centre Régional de Lutte contre le Cancer Oscar Lambret [Lille] (UNICANCER/Lille), Université de Lille-UNICANCER, Laboratory for Integrated Micro Mechatronics Systems (LIMMS), The University of Tokyo (UTokyo)-Centre National de la Recherche Scientifique (CNRS), Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), NanoBioInterfaces - IEMN (NBI - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Pathogenèse virale du diabète de type 1 - ULR 3610 (Laboratoire de Virologie), Centre d’Infection et d’Immunité de Lille - INSERM U 1019 - UMR 9017 - UMR 8204 (CIIL), Institut Pasteur de Lille, Réseau International des Instituts Pasteur (RIIP)-Réseau International des Instituts Pasteur (RIIP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Centre National de la Recherche Scientifique (CNRS), The authors thank B. Guerred, S. Menasria and S. Miloudi for excellent technical assistance. They acknowledge the work of technicians and engineers of the Biology and Pathology Center of the Lille University Hospital (CHU Lille) who are involved in the diagnostics of SARS-CoV-2. This research was supported by I-SITE ULNE, the Centre Hospitalier Universitaire de Lille and Université de Lille., and IEMN, Collection
Subjects: [SPI]Engineering Sciences [physics], [SPI] Engineering Sciences [physics], ComputingMilieux_MISCELLANEOUS
Abstract: International audience
Published: 2022

28. MAGMA: Inference and Prediction using Multi-Task Gaussian Processes with Common Mean

Author: Arthur Leroy, Pierre Latouche, Benjamin Guedj, Servane Gey, Department of Computer Science [Sheffield], University of Sheffield [Sheffield], Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), Benjamin Guedj acknowledges partial support by the U.S. Army Research Laboratory and the U.S. Army Research Office, and by the U.K. Ministry of Defence and the U.K. Engineering and Physical Sciences Research Council (EPSRC) under grant number EP/R013616, ANR-18-CE40-0016,BEAGLE,Apprentissage PAC-bayésien agnostique(2018), and ANR-18-CE23-0015,APRIORI,Une Perspective PAC-Bayésienne de l'Apprentissage de Représentations(2018)
Subjects: Functional data analysis, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Artificial Intelligence, Multi-task learning, Common mean process, Gaussian process, EM algorithm, [STAT.CO]Statistics [stat]/Computation [stat.CO], [STAT.ME]Statistics [stat]/Methodology [stat.ME], Software
Abstract: A novel multi-task Gaussian process (GP) framework is proposed, by using a common mean process for sharing information across tasks. In particular, we investigate the problem of time series forecasting, with the objective to improve multiple-step-ahead predictions. The common mean process is defined as a GP for which the hyper-posterior distribution is tractable. Therefore an EM algorithm is derived for handling both hyper-parameters optimisation and hyper-posterior computation. Unlike previous approaches in the literature, the model fully accounts for uncertainty and can handle irregular grids of observations while maintaining explicit formulations, by modelling the mean process in a unified GP framework. Predictive analytical equations are provided, integrating information shared across tasks through a relevant prior mean. This approach greatly improves the predictive performances, even far from observations, and may reduce significantly the computational complexity compared to traditional multi-task GP models. Our overall algorithm is called Magma (standing for Multi tAsk GPs with common MeAn). The quality of the mean process estimation, predictive performances, and comparisons to alternatives are assessed in various simulated scenarios and on real datasets.
Published: 2022

29. Predictive model for airborne insect abundance intercepted by a continuous wave Scheimpflug lidar in relation to meteorological parameters

Author: Gbogbo, Adolphe, Kouakou, Benoît, Dabo-Niang, Sophie, Zoueu, Jérémie, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: Computational Theory and Mathematics, Ecology, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Applied Mathematics, Ecological Modeling, Modeling and Simulation, Ecology, Evolution, Behavior and Systematics, ComputingMilieux_MISCELLANEOUS, Computer Science Applications
Abstract: International audience
Published: 2022

30. On PAC-Bayesian reconstruction guarantees for VAEs

Author: Cherief-Abdellatif, B-E, Shi, Y, Doucet, A, Guedj, B, University of Oxford, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Partial support from the French National Agency for Research, grants ANR-18-CE40-0016-01 and ANR-18-CE23-0015-02
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Computer Vision and Pattern Recognition (cs.CV), Computer Science - Computer Vision and Pattern Recognition, FOS: Mathematics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Machine Learning (cs.LG)
Abstract: Despite its wide use and empirical successes, the theoretical understanding and study of the behaviour and performance of the variational autoencoder (VAE) have only emerged in the past few years. We contribute to this recent line of work by analysing the VAE's reconstruction ability for unseen test data, leveraging arguments from the PAC-Bayes theory. We provide generalisation bounds on the theoretical reconstruction error, and provide insights on the regularisation effect of VAE objectives. We illustrate our theoretical results with supporting experiments on classical benchmark datasets., Comment: 14 pages
Published: 2022

31. A New Probabilistic Representation of the Alternating Zeta Function and a New Selberg-like Integral Evaluation

Author: Iovleff, Serge, Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS), MOdel for Data Analysis and Learning (MODAL), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Université de Technologie de Belfort-Montbeliard (UTBM)
Subjects: [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Classical Analysis and ODEs, Probability (math.PR), Classical Analysis and ODEs (math.CA), FOS: Mathematics, [MATH.MATH-CA]Mathematics [math]/Classical Analysis and ODEs [math.CA], Mathematics - Probability
Abstract: In this paper, we present two new representations of the alternating Zeta function. We show that for any s $\in$ C this function can be computed as a limit of a series of determinant. We then express these determinants as the expectation of a functional of a random vector with Dixon-Anderson density. The generalization of this representation to more general alternating series allows us to evaluate a Selberg-type integral with a generalized Vandermonde determinant.
Published: 2022

32. Interpretable Domain Adaptation for Hidden Subdomain Alignment in the Context of Pre-trained Source Models

Author: Zhang, Luxin, Germain, Pascal, Kessaci, Yacine, Biernacki, Christophe, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Worldline France, Université Laval [Québec] (ULaval), Biernacki, Christophe, RD Worldline, and Institut National de Recherche en Informatique et en Automatique (Inria)
Subjects: [STAT.ME] Statistics [stat]/Methodology [stat.ME], General Medicine, [STAT.ME]Statistics [stat]/Methodology [stat.ME]
Abstract: Domain adaptation aims to leverage source domain knowledge to predict target domain labels. Most domain adaptation methods tackle a single-source, single-target scenario, whereas source and target domain data can often be subdivided into data from different distributions in real-life applications (e.g., when the distribution of the collected data changes with time). However, such subdomains are rarely given and should be discovered automatically. To this end, some recent domain adaptation works seek separations of hidden subdomains, w.r.t. a known or fixed number of subdomains. In contrast, this paper introduces a new subdomain combination method that leverages a variable number of subdomains. Precisely, we propose to use an inter-subdomain divergence maximization criterion to exploit hidden subdomains. Besides, our proposition stands in a target-to-source domain adaptation scenario, where one exploits a pre-trained source model as a black box; thus, the proposed method is model-agnostic. By providing interpretability at two complementary levels (transformation and subdomain levels), our method can also be easily interpreted by practitioners with or without machine learning backgrounds. Experimental results over two fraud detection datasets demonstrate the efficiency of our method.
Published: 2022

33. Non-Vacuous Generalisation Bounds for Shallow Neural Networks

Author: Biggs, Felix, Guedj, Benjamin, Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), The Alan Turing Institute, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Machine Learning (stat.ML), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Machine Learning (cs.LG)
Abstract: We focus on a specific class of shallow neural networks with a single hidden layer, namely those with $L_2$-normalised data and either a sigmoid-shaped Gaussian error function ("erf") activation or a Gaussian Error Linear Unit (GELU) activation. For these networks, we derive new generalisation bounds through the PAC-Bayesian theory; unlike most existing such bounds they apply to neural networks with deterministic rather than randomised parameters. Our bounds are empirically non-vacuous when the network is trained with vanilla stochastic gradient descent on MNIST and Fashion-MNIST., 19 pages, 12 figures
Published: 2022

34. KSD Aggregated Goodness-of-fit Test

Author: Schrab, Antonin, Guedj, Benjamin, Gretton, Arthur, Gatsby Computational Neuroscience Unit, University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and The Alan Turing Institute
Subjects: Methodology (stat.ME), FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, FOS: Mathematics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Statistics - Methodology, Machine Learning (cs.LG)
Abstract: We investigate properties of goodness-of-fit tests based on the Kernel Stein Discrepancy (KSD). We introduce a strategy to construct a test, called KSDAgg, which aggregates multiple tests with different kernels. KSDAgg avoids splitting the data to perform kernel selection (which leads to a loss in test power), and rather maximises the test power over a collection of kernels. We provide non-asymptotic guarantees on the power of KSDAgg: we show it achieves the smallest uniform separation rate of the collection, up to a logarithmic term. For compactly supported densities with bounded model score function, we derive the rate for KSDAgg over restricted Sobolev balls; this rate corresponds to the minimax optimal rate over unrestricted Sobolev balls, up to an iterated logarithmic term. KSDAgg can be computed exactly in practice as it relies either on a parametric bootstrap or on a wild bootstrap to estimate the quantiles and the level corrections. In particular, for the crucial choice of bandwidth of a fixed kernel, it avoids resorting to arbitrary heuristics (such as median or standard deviation) or to data splitting. We find on both synthetic and real-world data that KSDAgg outperforms other state-of-the-art quadratic-time adaptive KSD-based goodness-of-fit testing procedures., Comment: 27 pages, 3 figures
Published: 2022

35. Asymptotic efficiency of some nonparametric tests for location on hyperspheres

Author: Sophie Dabo-Niang, Baba Thiam, Thomas Verdebout, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Dabo-Niang, Sophie
Subjects: Statistics and Probability, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Probability and Uncertainty, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Published: 2022

36. Investigating spatial scan statistics for multivariate functional data

Author: Camille Frévent, Mohamed-Salem Ahmed, Sophie Dabo-Niang, Michaël Genin, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Dabo-Niang, Sophie
Subjects: Statistics and Probability, Methodology (stat.ME), FOS: Computer and information sciences, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Statistics, Probability and Uncertainty, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Statistics - Methodology
Abstract: This paper introduces new scan statistics for multivariate functional data indexed in space. The new methods are derivated from a MANOVA test statistic for functional data, an adaptation of the Hotelling T2-test statistic, and a multivariate extension of the Wilcoxon rank-sum test statistic. In a simulation study, the latter two methods present very good performances and the adaptation of the functional MANOVA also shows good performances for a normal distribution. Our methods detect more accurate spatial clusters than an existing nonparametric functional scan statistic. Lastly we applied the methods on multivariate functional data to search for spatial clusters of abnormal daily concentrations of air pollutants in the north of France in May and June 2020., Comment: arXiv admin note: text overlap with arXiv:2011.03482
Published: 2022

37. Modelling Spatially Clustered Failure Time Data via Multivariate Gaussian Random Fields

Author: Sainul, Fathima, Dabo-Niang, Sophie, Adekpedjou, Akim, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Dabo-Niang, Sophie
Subjects: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Published: 2022

38. An estimation framework for the influential-imitator diffusion

Author: Nasini, Stefano, Tchouya, Thomas Ringo, Dabo-Niang, Sophie, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Dabo-Niang, Sophie
Subjects: History, Polymers and Plastics, [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], Business and International Management, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST], Industrial and Manufacturing Engineering
Published: 2022

39. K-nearest neighbors method estimation of regression function for spatial dependent data

Author: Ahmed, Mohamed Salem, Attouch, Mohamed, Dabo-Niang, Sophie, Ndiaye, Mamadou, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), and Dabo-Niang, Sophie
Subjects: [MATH.MATH-ST]Mathematics [math]/Statistics [math.ST], [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST]
Published: 2022

40. Dynamic Ranking with the BTL Model: A Nearest Neighbor based Rank Centrality Method

Author: Karlé, Eglantine, Tyagi, Hemant, Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Laboratoire Paul Painlevé - UMR 8524 (LPP), and Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe
Subjects: FOS: Computer and information sciences, [STAT]Statistics [stat], Statistics - Machine Learning, FOS: Mathematics, Mathematics - Statistics Theory, Machine Learning (stat.ML), Statistics Theory (math.ST), [MATH]Mathematics [math]
Abstract: Many applications such as recommendation systems or sports tournaments involve pairwise comparisons within a collection of $n$ items, the goal being to aggregate the binary outcomes of the comparisons in order to recover the latent strength and/or global ranking of the items. In recent years, this problem has received significant interest from a theoretical perspective with a number of methods being proposed, along with associated statistical guarantees under the assumption of a suitable generative model. While these results typically collect the pairwise comparisons as one comparison graph $G$, however in many applications - such as the outcomes of soccer matches during a tournament - the nature of pairwise outcomes can evolve with time. Theoretical results for such a dynamic setting are relatively limited compared to the aforementioned static setting. We study in this paper an extension of the classic BTL (Bradley-Terry-Luce) model for the static setting to our dynamic setup under the assumption that the probabilities of the pairwise outcomes evolve smoothly over the time domain $[0,1]$. Given a sequence of comparison graphs $(G_{t'})_{t' \in \mathcal{T}}$ on a regular grid $\mathcal{T} \subset [0,1]$, we aim at recovering the latent strengths of the items $w_t^* \in \mathbb{R}^n$ at any time $t \in [0,1]$. To this end, we adapt the Rank Centrality method - a popular spectral approach for ranking in the static case - by locally averaging the available data on a suitable neighborhood of $t$. When $(G_{t'})_{t' \in \mathcal{T}}$ is a sequence of Erd\"os-Renyi graphs, we provide non-asymptotic $\ell_2$ and $\ell_{\infty}$ error bounds for estimating $w_t^*$ which in particular establishes the consistency of this method in terms of $n$, and the grid size $\lvert\mathcal{T}\rvert$. We also complement our theoretical analysis with experiments on real and synthetic data., Comment: 52 pages, 5 figures, 4 tables, revised as per reviewer comments, added section 3.3 and additional experiment results
Published: 2022

41. Single cell classification using statistical learning on mechanical properties measured by mems tweezers

Author: Ahmadian, Bahram, Mbujamba, Deborah, Gerbedoen, Jean Claude, Kumemura, Momoko, Fujita, Hiroyuki, Collard, Dominique, Dabo-Niang, Sophie, Lagadec, Chann, Tarhan, Mehmet, Institut d’Électronique, de Microélectronique et de Nanotechnologie - UMR 8520 (IEMN), Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), Université catholique de Lille (UCL)-Université catholique de Lille (UCL), Bio-Micro-Electro-Mechanical Systems - IEMN (BIOMEMS - IEMN), Université catholique de Lille (UCL)-Université catholique de Lille (UCL)-Centrale Lille-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université Polytechnique Hauts-de-France (UPHF)-JUNIA (JUNIA), JUNIA (JUNIA), Université catholique de Lille (UCL), Laboratory for Integrated Micro Mechatronics Systems (LIMMS), The University of Tokyo (UTokyo)-Centre National de la Recherche Scientifique (CNRS), Kyushu Institute of Technology (Kyutech), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Cancer Heterogeneity, Plasticity and Resistance to Therapies - UMR 9020 - U 1277 (CANTHER), Institut Pasteur de Lille, Réseau International des Instituts Pasteur (RIIP)-Réseau International des Instituts Pasteur (RIIP)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Centre National de la Recherche Scientifique (CNRS), This work is in the framework of SMMiL-E activities (a joint project of CNRS, Institute of Industrial Science, Centre Oscar Lambret and University of Lille) and supported by a grant from Contrat de Plan Etat-Region CPER Cancer 2015–2020, and Ruban Rose award. The authors acknowledge IRCL for hosting SMMiL-E. M. C. Tarhan acknowledge I-SITE ULNE., Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille, his work is in the framework of SMMiL-E activities (a joint project of CNRS, Institute of Industrial Science, Centre Oscar Lambret and University of Lille) and supported by a grant from Contrat de Plan Etat-Region CPER Cancer 2015–2020, and Ruban Rose award. The authors acknowledge IRCL for hosting SMMiL-E. M. C. Tarhan acknowledge I-SITE ULNE., and Dabo-Niang, Sophie
Subjects: [STAT]Statistics [stat], cancer cell classification, [SPI]Engineering Sciences [physics], Single-cell characterization, [SPI] Engineering Sciences [physics], MEMS tweezers, supervised learning, [STAT] Statistics [stat]
Abstract: International audience; Cell population is heterogenous and so presents a wide range of properties as metastatic potential. But using rare cells for clinical applications requires precise classification of individual cells. Here, we propose a multi-parameter analysis of single cells to classify them using statistical learning techniques and to predict the sub-population of each cell, although they may have close characteristics. We used MEMS tweezers to analyze mechanical properties (stiffness, viscosity, and size) of single cells from two different breast cancer cell lines in a controlled environment and run supervised learning methods to predict the population they belong to. This label-free method is a significant step forward to distinguish rare cell sub-populations for clinical applications.
Published: 2022

42. Fondamentaux de l’IA et domaines d’application

Author: Biernacki, Christophe, Biernacki, Christophe, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: [STAT]Statistics [stat], [STAT] Statistics [stat]
Abstract: National audience
Published: 2022

43. Conditional tail and quantile estimation for real-valued β-mixing spatial data

Author: Tchazino, Tchamiè, Diop, Aliou, Dabo-Niang, Sophie, Tchazino, Tchamiè, Université d’Abomey-Calavi = University of Abomey Calavi (UAC), University Gaston Berger, LERSTAD, Saint-Louis, Senegal (UGB), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: [STAT]Statistics [stat], spatial dependence, Asymptotic normality, conditional extreme value index, β-mixing, functional estimation, bias correction, [STAT] Statistics [stat]
Abstract: This paper deals with the estimation of the tail index of a conditionnal heavy-tailed distribution of a spatial process. We are particularly interested in the estimation of conditionnal spatial rare events when the process is β−mixing. Given a conditionnal stationary real-valued multidimensional spatial process Y x i , i ∈ Z N , we investigate its conditional heavy-tail index estimation and the corresponding conditional quantile. Asymptotic properties of the corresponding estimators are established under mild mixing conditions. The particularity of the tail proposed estimator is based on the spatial nature of the sample and its unbiased and reduced variance properties compared to well known conditional tail index estimators. A numerical study on synthetic and real datasets is conducted to assess the finite-sample behaviour of the proposed estimators.
Published: 2022

44. An end-to-end data-driven optimisation framework for constrained trajectories

Author: Florent Dewez, Benjamin Guedj, Arthur Talpaert, Vincent Vandewalle, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut National de Recherche en Informatique et en Automatique (Inria), Inria Lille - Nord Europe, The Alan Turing Institute, Université de Lille, Laboratoire Paul Painlevé - UMR 8524 (LPP), and Computer science department [University College London] (UCL-CS)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.AP]Statistics [stat]/Applications [stat.AP], Constrained optimisation Contents, Machine Learning (stat.ML), Statistics - Applications, Functional data, Machine Learning (cs.LG), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Optimization and Control (math.OC), FOS: Mathematics, Applications (stat.AP), [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC], Statistical modelling, Mathematics - Optimization and Control
Abstract: Many real-world problems require to optimise trajectories under constraints. Classical approaches are based on optimal control methods but require an exact knowledge of the underlying dynamics, which could be challenging or even out of reach. In this paper, we leverage data-driven approaches to design a new end-to-end framework which is dynamics-free for optimised and realistic trajectories. We first decompose the trajectories on function basis, trading the initial infinite dimension problem on a multivariate functional space for a parameter optimisation problem. A maximum \emph{a posteriori} approach which incorporates information from data is used to obtain a new optimisation problem which is regularised. The penalised term focuses the search on a region centered on data and includes estimated linear constraints in the problem. We apply our data-driven approach to two settings in aeronautics and sailing routes optimisation, yielding commanding results. The developed approach has been implemented in the Python library PyRotor., Comment: 28 pages
Published: 2022

45. Impact of missing data on mixtures and clustering with illustrations in Biology and Medicine

Author: Biernacki, Christophe, Biernacki, Christophe, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: [STAT]Statistics [stat], [STAT] Statistics [stat]
Abstract: National audience
Published: 2022

46. PAC-Bayes Generalisation Bounds for Heavy-Tailed Losses through Supermartingales

Author: Haddouche, Maxime, Guedj, Benjamin, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), The Inria London Programme (Inria-London), Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), University College of London [London] (UCL), and The Alan Turing Institute
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, generalisation bounds, Mathematics - Statistics Theory, unbounded losses, Machine Learning (stat.ML), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Statistics Theory (math.ST), Machine Learning (cs.LG), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, FOS: Mathematics, PAC-Bayes, supermartingales
Abstract: While PAC-Bayes is now an established learning framework for light-tailed losses (\emph{e.g.}, subgaussian or subexponential), its extension to the case of heavy-tailed losses remains largely uncharted and has attracted a growing interest in recent years. We contribute PAC-Bayes generalisation bounds for heavy-tailed losses under the sole assumption of bounded variance of the loss function. Under that assumption, we extend previous results from \citet{kuzborskij2019efron}. Our key technical contribution is exploiting an extention of Markov's inequality for supermartingales. Our proof technique unifies and extends different PAC-Bayesian frameworks by providing bounds for unbounded martingales as well as bounds for batch and online learning with heavy-tailed losses., Comment: New Section 3 on Online PAC-Bayes
Published: 2022
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47. Model-based Clustering with Missing Not At Random Data

Author: Sportisse, Aude, Biernacki, Christophe, Boyer, Claire, Josse, Julie, Marbac Lourdelle, Matthieu, Celeux, Gilles, Laporte, Fabien, Université Côte d'Azur (UCA), Modèles et algorithmes pour l’intelligence artificielle (MAASAI), Inria Sophia Antipolis - Méditerranée (CRISAM), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Laboratoire Jean Alexandre Dieudonné (JAD), Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Scalable and Pervasive softwARe and Knowledge Systems (Laboratoire I3S - SPARKS), Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (1965 - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Laboratoire d'Informatique, Signaux, et Systèmes de Sophia Antipolis (I3S), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS), Université de Rennes (UNIV-RENNES), Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] (ENSAI), Centre National de la Recherche Scientifique (CNRS), Centre de Recherche en Economie et Statistique [Bruz] (CREST), Université Lille Nord (France), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé - UMR 8524 (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), Sorbonne Université (SU), Laboratoire de Probabilités, Statistique et Modélisation (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales (MOKAPLAN), CEntre de REcherches en MAthématiques de la DEcision (CEREMADE), Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Institut Desbrest de santé publique (IDESP), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Médecine de précision par intégration de données et inférence causale (PREMEDICAL), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Institut Desbrest de santé publique (IDESP), Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Université de Montpellier (UM), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria), Université Paris-Saclay, Nantes Université (Nantes Univ), Institut du Thorax [Nantes], INSERM U649, Nantes, Institut National de la Santé et de la Recherche Médicale (INSERM), ANR-19-P3IA-0002,3IA@cote d'azur,3IA Côte d'Azur(2019), ANR-16-IDEX-0006,MUSE,MUSE(2016), Inria Lille - Nord Europe, Université Catholique de l'Ouest (UCO), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Laboratoire Jean Alexandre Dieudonné (LJAD), Université de Rennes (UR), Laboratoire Paul Painlevé (LPP), Statistique mathématique et apprentissage (CELESTE), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Université Nice Sophia Antipolis (... - 2019) (UNS), Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Centre National de la Recherche Scientifique (CNRS)-Scalable and Pervasive softwARe and Knowledge Systems (Laboratoire I3S - SPARKS), Université Nice Sophia Antipolis (... - 2019) (UNS), COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-COMUE Université Côte d'Azur (2015-2019) (COMUE UCA)-Centre National de la Recherche Scientifique (CNRS)-Université Côte d'Azur (UCA)-Université Nice Sophia Antipolis (... - 2019) (UNS), Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Paul Painlevé - UMR 8524 (LPP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-École polytechnique universitaire de Lille (Polytech Lille)-Université de Lille, Sciences et Technologies, Laboratoire de Probabilités, Statistiques et Modélisations (LPSM (UMR_8001)), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPC), Centre National de la Recherche Scientifique (CNRS)-Université Paris Dauphine-PSL, and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Inria de Paris
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, Missing Not At Random (MNAR) Data, Model-based Clustering, Machine Learning (stat.ML), Identifiability, EM and Stochastic EM Algorithms, Machine Learning (cs.LG), Medical Data
Abstract: In recent decades, technological advances have made it possible to collect large data sets. In this context, the model-based clustering is a very popular, flexible and interpretable methodology for data exploration in a well-defined statistical framework. One of the ironies of the increase of large datasets is that missing values are more frequent. However, traditional ways (as discarding observations with missing values or imputation methods) are not designed for the clustering purpose. In addition, they rarely apply to the general case, though frequent in practice, of Missing Not At Random (MNAR) values, i.e. when the missingness depends on the unobserved data values and possibly on the observed data values. The goal of this paper is to propose a novel approach by embedding MNAR data directly within model-based clustering algorithms. We introduce a selection model for the joint distribution of data and missing-data indicator. It corresponds to a mixture model for the data distribution and a general MNAR model for the missing-data mechanism, which may depend on the underlying classes (unknown) and/or the values of the missing variables themselves. A large set of meaningful MNAR sub-models is derived and the identifiability of the parameters is studied for each of the sub-models, which is usually a key issue for any MNAR proposals. The EM and Stochastic EM algorithms are considered for estimation. Finally, we perform empirical evaluations for the proposed submodels on synthetic data and we illustrate the relevance of our method on a medical register, the TraumaBase ® dataset.
Published: 2022

48. Cluster-Specific Predictions with Multi-Task Gaussian Processes

Author: Leroy, Arthur, Latouche, Pierre, Guedj, Benjamin, Gey, Servane, University of Manchester [Manchester], Mathématiques Appliquées Paris 5 (MAP5 - UMR 8145), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité), University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Inria-CWI (Inria-CWI), Centrum Wiskunde & Informatica (CWI)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), Engineering and Physical Sciences Research Council (EPSRC), grant number EP/R013616/1, ANR-18-CE40-0016,BEAGLE,Apprentissage PAC-bayésien agnostique(2018), ANR-18-CE23-0015,APRIORI,Une Perspective PAC-Bayésienne de l'Apprentissage de Représentations(2018), Computer science department [University College London] (UCL-CS), Laboratoire Paul Painlevé - UMR 8524 (LPP), Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-École polytechnique universitaire de Lille (Polytech Lille), and Institut National des Sciences Mathématiques et de leurs Interactions (INSMI)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPC)
Subjects: FOS: Computer and information sciences, cluster-specific predictions, Computer Science - Machine Learning, Gaussian processes mixture, multi-task learning, Machine Learning (stat.ML), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], curve clustering, Statistics - Computation, variational EM, Machine Learning (cs.LG), Methodology (stat.ME), [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, [STAT.CO]Statistics [stat]/Computation [stat.CO], Computation (stat.CO), Statistics - Methodology
Abstract: A model involving Gaussian processes (GPs) is introduced to simultaneously handle multi-task learning, clustering, and prediction for multiple functional data. This procedure acts as a model-based clustering method for functional data as well as a learning step for subsequent predictions for new tasks. The model is instantiated as a mixture of multi-task GPs with common mean processes. A variational EM algorithm is derived for dealing with the optimisation of the hyper-parameters along with the hyper-posteriors' estimation of latent variables and processes. We establish explicit formulas for integrating the mean processes and the latent clustering variables within a predictive distribution, accounting for uncertainty on both aspects. This distribution is defined as a mixture of cluster-specific GP predictions, which enhances the performances when dealing with group-structured data. The model handles irregular grid of observations and offers different hypotheses on the covariance structure for sharing additional information across tasks. The performances on both clustering and prediction tasks are assessed through various simulated scenarios and real datasets. The overall algorithm, called MagmaClust, is publicly available as an R package., 47 pages
Published: 2022

49. Reprint: a randomized extrapolation based on principal components for data augmentation

Author: Wei, Jiale, Chen, Qiyuan, Peng, Pai, Guedj, Benjamin, Li, Le, Guedj, Benjamin, Central China Normal University [Wuhan, China], University College of London [London] (UCL), Department of Computer science [University College of London] (UCL-CS), Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria), The Alan Turing Institute, The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille), National Natural Science Foundation of China (Grant No. 62107021), and Hubei ProvincialScience and Technology Innovation Base (Platform) Special Project 2020DFH002
Subjects: FOS: Computer and information sciences, History, Computer Science - Computation and Language, Principal components, Polymers and Plastics, Data augmentation, Hidden-space representation, [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], Randomised extrapolation, Industrial and Manufacturing Engineering, [INFO.INFO-CL]Computer Science [cs]/Computation and Language [cs.CL], [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-CL] Computer Science [cs]/Computation and Language [cs.CL], Business and International Management, Computation and Language (cs.CL)
Abstract: Data scarcity and data imbalance have attracted a lot of attention in many fields. Data augmentation, explored as an effective approach to tackle them, can improve the robustness and efficiency of classification models by generating new samples. This paper presents REPRINT, a simple and effective hidden-space data augmentation method for imbalanced data classification. Given hidden-space representations of samples in each class, REPRINT extrapolates, in a randomized fashion, augmented examples for target class by using subspaces spanned by principal components to summarize distribution structure of both source and target class. Consequently, the examples generated would diversify the target while maintaining the original geometry of target distribution. Besides, this method involves a label refinement component which allows to synthesize new soft labels for augmented examples. Compared with different NLP data augmentation approaches under a range of data imbalanced scenarios on four text classification benchmark, REPRINT shows prominent improvements. Moreover, through comprehensive ablation studies, we show that label refinement is better than label-preserving for augmented examples, and that our method suggests stable and consistent improvements in terms of suitable choices of principal components. Moreover, REPRINT is appealing for its easy-to-use since it contains only one hyperparameter determining the dimension of subspace and requires low computational resource.
Published: 2022
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50. Controlling Confusion via Generalisation Bounds

Author: Adams, Reuben, Shawe-Taylor, John, Guedj, Benjamin, Department of Computer science [University College of London] (UCL-CS), University College of London [London] (UCL), The Inria London Programme (Inria-London), University College of London [London] (UCL)-University College of London [London] (UCL)-Institut National de Recherche en Informatique et en Automatique (Inria), The Alan Turing Institute, MOdel for Data Analysis and Learning (MODAL), Laboratoire Paul Painlevé (LPP), Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille-Centre National de la Recherche Scientifique (CNRS)-Université de Lille, Sciences et Technologies-Inria Lille - Nord Europe, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Evaluation des technologies de santé et des pratiques médicales - ULR 2694 (METRICS), and Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-Université de Lille-Centre Hospitalier Régional Universitaire [Lille] (CHRU Lille)-École polytechnique universitaire de Lille (Polytech Lille)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, PAC-Bayes theory, Mathematics - Statistics Theory, Machine Learning (stat.ML), [STAT.TH]Statistics [stat]/Statistics Theory [stat.TH], Statistics Theory (math.ST), Classification, Machine Learning (cs.LG), ComputingMethodologies_PATTERNRECOGNITION, [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], Statistics - Machine Learning, FOS: Mathematics, Statistical Learning Theory, Generalisation Bounds
Abstract: We establish new generalisation bounds for multiclass classification by abstracting to a more general setting of discretised error types. Extending the PAC-Bayes theory, we are hence able to provide fine-grained bounds on performance for multiclass classification, as well as applications to other learning problems including discretisation of regression losses. Tractable training objectives are derived from the bounds. The bounds are uniform over all weightings of the discretised error types and thus can be used to bound weightings not foreseen at training, including the full confusion matrix in the multiclass classification case., Comment: 31 pages
Published: 2022
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