Program and abstracts

Wednesday, 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.

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, TBA

12:00-13:30 Lunch

13:30-14:30 Gilles Blanchard, TBA

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, TBA

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
related to the concentration of measure phenomenon, chosen for being
remarkable and inspiring, highlighting their contemporary resonances. This
involves spheres, shells, high-dimensional geometry, transportation, and, if
time permits, a bit of stochastic calculus. The talk is intended to be
accessible, with the emphasis on the concepts and ideas.

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.

We then conclude with the case of exponential rather than Gaussian noise, for which the complexity of the problem is governed by the behavior of certain Bernoulli processes. When combined with the Bednorz-Latała theorem confirming Talagrand's Bernoulli conjecture, this implies a decomposition theorem that characterizes the optimal error in terms of both the $\ell^1$ and $\ell^2$ metric structures of the parameter set.

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, TBA

Gilles Blanchard, TBA

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, TBA