Lieu : IHP, amphi Darboux
14.00 : Marie Perrot-Dockes (Université de Paris),
Titre : Inférence après sélection du taux de faux positifs dans un modèle de Markov caché
Résumé : We address the multiple testing problem under the assumption that the true/false hypotheses are driven by a Hidden Markov Model (HMM), which is recognized as a fundamental setting to model multiple testing under dependence since the seminal work of Sun and Cai 2009. While previous work has concentrated on deriving specific procedures with a controlled False Discovery Rate (FDR) under this model, following a recent trend in selective inference, we consider the problem of establishing confidence bounds on the false discovery proportion (FDP), for a user-selected set of hypotheses that can depend on the observed data in an arbitrary way. We develop a methodology to construct such confidence bounds first when the HMM model is known, then when its parameters are unknown and estimated, including the data distribution under the null and the alternative, using a nonparametric approach. In the latter case, we propose a bootstrap-based methodology to take into account the effect of parameter estimation error. We show that taking advantage of the assumed HMM structure allows for a substantial improvement of confidence bound sharpness over existing agnostic (structure-free) methods, as witnessed both via numerical experiments and real data examples.
15.00 : Angelina Roche (Université Paris Dauphine)
Titre : Sparsité dans le modèle linéaire fonctionnel multivarié
Résumé : L'objectif de cet exposé est d'étudier une procédure d'estimation parcimonieuse dans un problème de régression linéaire prenant en entrée un vecteur de covariables qui peuvent être de différentes natures (vecteurs et/ou données fonctionnelles). Deux estimateurs de type Lasso seront considérés et comparés d'un point de vue théorique et pratique. Cette présentation soulèvera également la question de la nécessité ou non de projeter/régulariser les données fonctionnelles. Une application à la prédiction de la consommation d'électricité sera présentée.
16.00 : Joon Kwon (INRAE & AgroParisTech)
Titre : Refined approachability algorithms and application to regret minimization with global costs
Résumé : Blackwell's approachability is a framework where two players, the Decision Maker and the Environment, play a repeated game with vector-valued payoffs. The goal of the Decision Maker is to make the average payoff converge to a given set called the target. When this is indeed possible, simple algorithms which guarantee the convergence are known. This abstract tool was successfully used for the construction of optimal strategies in various repeated games, but also found several applications in online learning. By extending an approach proposed by (Abernethy et al., 2011), we construct and analyze a class of Follow the Regularized Leader algorithms (FTRL) for Blackwell's approachability which are able to minimize not only the Euclidean distance to the target set (as it is often the case in the context of Blackwell's approachability) but a wide range of distance-like quantities. This flexibility enables us to apply these algorithms to closely minimize the quantity of interest in various online learning problems. In particular, for regret minimization with ell_p global costs, we obtain the first bounds with explicit dependence in pand the dimension d.