|
7-9 janv. 2026 Orsay (France)
|
|
|
|
Program and abstractsWednesday, January 7, 2026 13:00-13:30 Welcome speech: Learning (and) statistics with Talagrand 13:30-15:00 Lecture 1.1 Pascal Massart: Concentration of probability measures explains cut-off phenomena in model selection: illustration in a simple setting 15:00-16:00 Jaouad Mourtada, From suprema of stochastic processes to sequential probability assignment 16:00-16:30 Coffee break 16:30-17:30 Fabienne Comte, A story of Probabilistic Inequalities for nonparametric estimation in regression and diffusion models. From 17:30 Cocktail
Thursday, January 8, 2026 9:00-10:30 Lecture 1.2 Pascal Massart, Concentration of probability measures explains cut-off phenomena in model selection: illustration in a simple setting 10:30-11:00 Coffee break 11:00-12:00 Anna Ben-Hamou, Proof and applications of the Convex Distance Inequality 12:00-13:30 Lunch 13:30-14:30 Gilles Blanchard, Estimating a large number of high-dimensional vector means 14:30-16:00 Lecture 2.1 Djalil Chafaï, Selected Topics around the Concentration of Measure 16:00-16:30 Coffee break 16:30-17:30 Sara van de Geer, A pivotal transform for the high-dimensional location scale model
Friday, January 9, 2026 9:00-10:30 Lecture 2.2 Djalil Chafaï, Selected Topics around the Concentration of Measure 10:30-11:00 Coffee break 11:00-12:00 Patricia Reynaud-Bouret, How to do estimation and model selection with learning data ? 12:00-13:30 Closing speech and lunch
Abstracts Courses: Pascal Massart, Concentration of probability measures explains cut-off phenomena in model selection: illustration in a simple setting This mini-course is made of two lectures. The first one will be devoted to a brief excursion in Michel Talagrand’s mathematics. The main purpose will be to revisit Talagrand’s view on the concentration of product probability measures and then derive concentration inequalities for non Gaussian chi-square type statistics from this abstract probabilistic material. During the second lecture we shall show how these inequalities can be used to shed light on cut-off phenomena for penalized least-squares criteria within a simple regression framework. The point of view and the results that we shall present here are mainly extracted from a recent joint paper with Vincent Rivoirard. Nothing revolutionary here, as everyone knows the impact that Talagrand's work has had on the development of mathematical statistics since the late 90s, but we've chosen a very simple framework in which everything can be explained with minimal technicality, leaving the main ideas to the fore. Djalil Chafaï, Selected Topics around the Concentration of Measure We plan to present elementary historical topics
Invited talks: Jaouad Mourtada, From suprema of stochastic processes to sequential probability assignment Michel Talagrand's seminal contributions to the study of suprema of stochastic processes provide a rich conceptual toolkit to analyze the complexity of high-dimensional estimation problems. In this talk, we focus on a prediction problem where ideas and results originating in Talagrand's theory of suprema of stochastic processes prove fruitful and admit natural analogues. Specifically, we discuss sequential probability assignment, where one aims to assign a high probability to a sequence of observations revealed one at a time. This problem is closely related to lossless data compression (universal coding) in information theory, and to next-token prediction in language models. We consider a Gaussian setting, in which the optimal error can be characterized in terms of certain geometric parameters of the parameter set. When combined with Talagrand's celebrated Majorizing Measures theorem, this implies an explicit characterization of the optimal error, of purely metric nature. We deduce that two basic obstructions (redundancy and noise correlation) suffice to determine the best achievable error. Fabienne Comte, A story of Probabilistic Inequalities for nonparametric estimation in regression and diffusion models. In this talk, I will explain how key probabilistic inequalities, namely Tropp Chernov and Talagrand deviation Ineqalities played a key role in the theoretical study of regression-type contrasts and improved both the assumptions and the statistical results related to nonparametric and adaptive estimators. Regression and diffusion models give various and interesting examples to illustrate this story, in different observation settings : discrete time with fixed unit step, high frequency for one diffusion path and continuous time data from independent paths. Anna Ben-Hamou, Proof and applications of the Convex Distance Inequality Talagrand’s Convex Distance Inequality is an isoperimetric inequality, which is emblematic of the concentration of measure phenomenon: in a product probability space, the probability to be at convex distance larger than $t$ from a given subset, multiplied by the probability of that subset, is less than $e^{-t^2/4}$. In this talk, we will give a proof which uses the transport method combined with couplings introduced by Katalin Marton. We will also give some applications of the inequality. Gilles Blanchard, Estimating a large number of high-dimensional vector means Joint work with Jean-Baptiste Fermanian and Hannah Marienwald. The problem of simultaneously estimating multiple means from independent samples has a long history in statistics, from the seminal works of Stein, Robbins in the 50s, Efron and Morris in the 70s and up to the present day. It can be also seen as an (extremely stylized) instance of "personalized federated learning" problem, where each user has their own data and target (the mean of their personal distribution), but potentially want to share some relevant information with "similar" users (though there is no information available a priori about which users are "similar"). In this talk I will concentrate on contributions to the high-dimensional case, where the samples and their means belong to R^d with "large" d. We focus on the role of the effective dimension of the data in a "dimensional asymptotics'' point of view, highlighting that the risk improvement of the proposed method satisfies an oracle inequality approaching an adaptive (minimax in a suitable sense) improvement as the effective dimension grows large. To achieve this, sharp concentration inequalities such as pioneered by M. Talagrand are an essential technical tool.
Sarah van de Geer, A pivotal transform for the high-dimensional location and scale model Joint work with Sylvain Sardy and Maxime van Cutsem. We study the high-dimensional linear model with noise distribution known up to a scale parameter. With an l1-penalty on the regression coefficients, we show that a transformation of the log-likelihood allows for a choice of the tuning parameter not depending on the scale parameter. This transformation is a generalization of the square root Lasso for quadratic loss. The tuning parameter can asymptotically be taken at the detection edge. To prove this we use the contraction inequality of Ledoux and Talagrand [1991]. This moreover leads to establishing asymptotic efficiency of the estimator of the scale parameter. Reference : M. Ledoux and M. Talagrand. Probability in Banach Spaces: Isoperimetry and Processes. Springer Verlag, New York, 1991. Patricia Reynaud-Bouret, How to do estimation and model sleection with learning data ? When a human or an animal is learning a task, the various choices and errors that itmakes are per essence non stationary and with strong dependance. However each individual is unique and it cannot learn twice. So to infer the cognitive strategy of the individual, we need to perform estimation and model selection for non stationnary strongly dependent data. Thanks to a new concentration inequality for suprema of renormalized martingales, we are able to show that Maximum Likelihood Esttimation and (variants of) Akaike criterion, which are the standard in computational behavioral analysis, might still work. This is a joint work with Julien Aubert, Luc Lehéricy, Louis Köhler, Giulia Mezzadri.
|
