pr\u00e9sentent<\/p>\n\n\n\n
Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en :<\/p>\n\n\n\n
le MERCREDI 11 D\u00e9CEMBRE 2024 \u00e0 14h00<\/p>\n\n\n\n
\u00e0 Amphith\u00e9\u00e2tre de DIGITEO
CEA Paris Saclay B\u00e2timent DIGITEO 565 91191 Gif-Sur-Yvette<\/p>\n\n\n\n
Membres du jury :<\/strong><\/p>\n\n\n\n M. Fran\u00e7ois DESBOUVRIES<\/strong>, Professeur, T\u00e9l\u00e9com SudParis, FRANCE – Directeur de these Invit\u00e9s :<\/strong><\/p>\n\n\n\n M. KAWASKI Eiji<\/strong>, Ing\u00e9nieur-Chercheur, CEA, FRANCE<\/p>\n\n\n\n M. BARAT Eric<\/strong>, Ing\u00e9nieur-Chercheur, CEA, FRANCE<\/p>\n\n\n\n R\u00e9sum\u00e9 :<\/strong><\/p>\n\n\n\n L’inf\u00e9rence bay\u00e9sienne a posteriori est utilis\u00e9e dans de nombreuses applications scientifiques et constitue une m\u00e9thodologie r\u00e9pandue pour la prise de d\u00e9cision en situation d’incertitude. Elle permet aux praticiens de confronter les observations du monde r\u00e9el \u00e0 des mod\u00e8les d’observation pertinents, et d’inf\u00e9rer en retour la distribution d’une variable explicative. Dans de nombreux domaines et applications pratiques, nous consid\u00e9rons des mod\u00e8les d’observation complexes pour leur pertinence scientifique, mais au prix de densit\u00e9s de probabilit\u00e9 incalculables. En cons\u00e9quence, \u00e0 la fois la vraisemblance et la distribution a posteriori sont indisponibles, rendant l’inf\u00e9rence Bay\u00e9sienne \u00e0 l’aide des m\u00e9thodes de Monte Carlo habituelles irr\u00e9alisable. Dans ce travail nous supposons que le mod\u00e8le d’observation nous g\u00e9n\u00e8re un jeu de donn\u00e9es, et le contexte de cette th\u00e8se est de coupler les m\u00e9thodes Bay\u00e9sienne \u00e0 l\u2019apprentissage statistique afin de pallier cette limitation et permettre l\u2019inf\u00e9rence a posteriori dans le cadre likelihood-free. Ce probl\u00e8me, formul\u00e9 comme l\u2019apprentissage d’une distribution de probabilit\u00e9, inclut les t\u00e2ches habituelles de classification et de r\u00e9gression, mais il peut \u00e9galement \u00eatre une alternative aux m\u00e9thodes \u201cApproximate Bayesian Computation\u201d dans le contexte de l’inf\u00e9rence bas\u00e9e sur la simulation, o\u00f9 le mod\u00e8le d’observation est un mod\u00e8le de simulation avec une densit\u00e9 implicite. L’objectif de cette th\u00e8se est de proposer des contributions m\u00e9thodologiques pour l’apprentissage Bay\u00e9sien a posteriori. Plus pr\u00e9cis\u00e9ment, notre objectif principal est de comparer diff\u00e9rentes m\u00e9thodes d’apprentissage dans le cadre de l’\u00e9chantillonnage Monte Carlo et de la quantification d\u2019incertitude. Nous consid\u00e9rons d’abord l’approximation a posteriori bas\u00e9e sur le \u201clikelihood-to-evidence-ratio\u201d, qui a l’avantage principal de transformer un probl\u00e8me d’apprentissage de densit\u00e9 conditionnelle en un probl\u00e8me de classification. Dans le contexte de l’\u00e9chantillonnage Monte Carlo, nous proposons une m\u00e9thodologie pour \u00e9chantillonner la distribution r\u00e9sultante d\u2019une telle approximation. Nous tirons parti de la structure sous-jacente du mod\u00e8le, compatible avec les algorithmes d’\u00e9chantillonnage usuels bas\u00e9s sur un quotient de densit\u00e9s, pour obtenir des proc\u00e9dures d’\u00e9chantillonnage simples, sans hyperparam\u00e8tre et ne n\u00e9cessitant d\u2019\u00e9valuer aucune densit\u00e9. Nous nous tournons ensuite vers le probl\u00e8me de la quantification de l’incertitude \u00e9pist\u00e9mique. D’une part, les mod\u00e8les normalis\u00e9s, tels que la construction discriminante, sont faciles \u00e0 appliquer dans le contexte de la quantification de l’incertitude bay\u00e9sienne. D’autre part, bien que les mod\u00e8les non normalis\u00e9s, comme le likelihood-to-evidence-ratio, ne soient pas facilement applicables dans les probl\u00e8mes de quantification d\u2019incertitude \u00e9pist\u00e9mique, une construction non normalis\u00e9e sp\u00e9cifique, que nous appelons g\u00e9n\u00e9rative, est effectivement compatible avec la quantification de l’incertitude bay\u00e9sienne via la distribution pr\u00e9dictive a posteriori. Dans ce contexte, nous expliquons comment r\u00e9aliser cette quantification de l’incertitude dans les deux techniques de mod\u00e9lisation, g\u00e9n\u00e9rative et discriminante, puis nous proposons une comparaison des deux constructions dans le cadre de l’apprentissage bay\u00e9sien. Enfin nous abordons le probl\u00e8me de la mod\u00e9lisation param\u00e9trique avec densit\u00e9 tractable, qui est effectivement un pr\u00e9requis pour la quantification de l’incertitude \u00e9pist\u00e9mique dans les m\u00e9thodes g\u00e9n\u00e9rative et discriminante. Nous proposons une nouvelle construction d’un mod\u00e8le param\u00e9trique, qui est une double extension des mod\u00e8les de m\u00e9lange et des flots normalisants. Ce mod\u00e8le peut \u00eatre appliqu\u00e9 \u00e0 de nombreux types de probl\u00e8mes statistiques, tels que l’inf\u00e9rence variationnelle, l’estimation de densit\u00e9 et de densit\u00e9 conditionnelle, car il b\u00e9n\u00e9ficie d’une \u00e9valuation rapide et exacte de la fonction de densit\u00e9, d’un sch\u00e9ma d’\u00e9chantillonnage simple, et d’une approche de reparam\u00e9trisation des gradients. Abstract :<\/strong><\/p>\n\n\n\n Bayesian posterior inference is used in many scientific applications and is a prevalent methodology for decision-making under uncertainty. It enables practitioners to confront real-world observations with relevant observation models, and in turn, infer the distribution over an explanatory variable. In many fields and practical applications, we consider ever more intricate observation models for their otherwise scientific relevance, but at the cost of intractable probability density functions. As a result, both the likelihood and the posterior are unavailable, making posterior inference using the usual Monte Carlo methods unfeasible. In this thesis, we suppose that the observation model provides a recorded dataset, and our aim is to bring together Bayesian inference and statistical learning methods to perform posterior inference in a likelihood-free setting. This problem, formulated as learning an approximation of a posterior distribution, includes the usual statistical learning tasks of regression and classification modeling, but it can also be an alternative to Approximate Bayesian Computation methods in the context of simulation-based inference, where the observation model is instead a simulation model with implicit density. The aim of this thesis is to propose methodological contributions for Bayesian posterior learning. More precisely, our main goal is to compare different learning methods under the scope of Monte Carlo sampling and uncertainty quantification. We first consider the posterior approximation based on the likelihood-to-evidence ratio, which has the main advantage that it turns a problem of conditional density learning into a problem of binary classification. In the context of Monte Carlo sampling, we propose a methodology for sampling from such a posterior approximation. We leverage the structure of the underlying model, which is conveniently compatible with the usual ratio-based sampling algorithms, to obtain straightforward, parameter-free, and density-free sampling procedures. We then turn to the problem of uncertainty quantification. On the one hand, normalized models such as the discriminative construction are easy to apply in the context of Bayesian uncertainty quantification. On the other hand, while unnormalized models, such as the likelihood-to-evidence-ratio, are not easily applied in uncertainty-aware learning tasks, a specific unnormalized construction, which we refer to as generative, is indeed compatible with Bayesian uncertainty quantification via the posterior predictive distribution. In this context, we explain how to carry out uncertainty quantification in both modeling techniques, and we then propose a comparison of the two constructions under the scope of Bayesian learning. We finally turn to the problem of parametric modeling with tractable density, which is indeed a requirement for epistemic uncertainty quantification in generative and discriminative modeling methods. We propose a new construction of a parametric model, which is an extension of both mixture models and normalizing flows. This model can be applied to many different types of statistical problems, such as variational inference, density estimation, and conditional density estimation, as it benefits from rapid and exact density evaluation, a straightforward sampling scheme, and a gradient reparameterization approach.<\/p>\n","protected":false},"excerpt":{"rendered":" L’Ecole doctorale : Math\u00e9matiques Hadamard et le Laboratoire de recherche SAMOVAR – Services r\u00e9partis, Architectures, Mod\u00e9lisation, Validation, Administration des R\u00e9seaux pr\u00e9sentent l\u2019AVIS DE SOUTENANCE de Monsieur Elouan ARGOUARC’H Autoris\u00e9 \u00e0 pr\u00e9senter ses travaux en vue de l\u2019obtention du Doctorat de l’Institut Polytechnique de Paris, pr\u00e9par\u00e9 \u00e0 T\u00e9l\u00e9com SudParis en : \u00ab Contributions \u00e0 l\u2019apprentissage statistique 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M. Guillaume CHARPIAT<\/strong>, Charg\u00e9 de recherche, INRIA Saclay, FRANCE – Examinateur
M. Mathilde MOUGEOT<\/strong>, Professeure, ENSIIE, FRANCE – Examinateur
M. Erwan LE PENNEC<\/strong>, Professeur, Ecole Polytechnique, FRANCE – Examinateur
M. Jean-Yves TOURNERET<\/strong>, Professeur, INP-ENSEEIHT Toulouse, FRANCE – Rapporteur
M. Fran\u00e7ois SEPTIER<\/strong>, Professeur, Universite Bretagne Sud, FRANCE – Rapporteur<\/p>\n\n\n\n\u00ab Contributions \u00e0 l\u2019apprentissage statistique de lois a posteriori pour l\u2019inf\u00e9rence bay\u00e9sienne sans vraisemblance \u00bb<\/h2>\n\n\n\n
pr\u00e9sent\u00e9 par Monsieur Elouan ARGOUARC’H<\/h2>\n\n\n\n
<\/p>\n\n\n\n