Organizing commitee : 

Karim Lounici  (CMAP, Ecole Polytechnique) and Katia Meziani (Ceremade,University Dauphine-PSL)

Program

Main lectures 

Baraud, Yannick: 

"The search of universal statisticalprocedures"

Tsybakov, Alexander B.

 One hour Talks

Akhavan, Arya: 

"Gradient-free optimization of highly smooth functions: passive and active schemes"

In this lecture, we delve into the study of zero-order optimization for a highly smooth, strongly convex function, examining it in two settings: passive and active schemes. In the passive scheme, we present an algorithm that utilizes local polynomial estimators to estimate the function's gradient and employs a projected gradient descent approach for optimization. In the active scheme, we propose a gradient estimator that relies on randomization within the \ell_1 ball. We demonstrate that our algorithms are nearly minimax optimal in both settings and provide a comprehensive comparison of the rates achieved under each design.

Brunel, Victor-Emmanuel:

 "Barycenters in metric spaces"

Barycenters, aka Fréchet means, offer a natural extension of averages from linear spaces to general metric spaces. Just as in Euclidean spaces, limit theorems (such as laws of large numbers and central limit theorems) are well known under fairly general assumptions. In this talk, after a brief introduction of barycenters in metric spaces, I will present a framework - that of geodesic spaces with non-positive curvature - where non-asymptotic guarantees can be proven. This talk is inspired from a recent work in collaboration with Jordan Serres (ENSAE).

Chérief-Abdellatif, Badr-Eddine : 

 "Label Shift Quantification via Distribution Feature Matching"

Quantification learning deals with the task of estimating the target label distribution under label shift. In this talk, we present a unifying framework, distribution feature matching (DFM), that recovers as particular instances various estimators introduced in previous literature. We derive a general performance bound for DFM procedures and extend this analysis to study robustness of DFM procedures in the misspecified setting under departure from the exact label shift hypothesis, in particular in the case of contamination of the target by an unknown distribution. We also illustrate the theoretical results with a numerical study.

Kostic, Vladimir: 

 "Learning time-homogenous Markov processes with Koopman operators : guarantees, benefits and challenges"

The integration of AI and Machine Learning (ML) techniques in scientific research has led to significant advancements in solving complex problems. One area that has gained prominence is the theory of Koopman operators, which provides a powerful tool for describing non-linear dynamical systems using associated linear operators. While data-driven algorithms for reconstructing Koopman operators are well-known, their connection to statistical learning remains largely unexplored. In this talk, we present a framework that utilizes reproducing kernel Hilbert spaces (RKHS) to learn Koopman operators from finite data trajectories. We establish high-probability finite-sample theoretical learning guarantees, ensuring the safe and trustworthy use of AI based on Koopman operator theory in scientific applications.

Besides presenting the classical study of excess risk bounds when learning with universal kernels, we develop non-asymptotic learning bounds for Koopman eigenvalues and eigenfunctions, making a significant contribution to the field. Specifically, we examine time-reversal-invariant stochastic dynamical systems, including Langevin dynamics, and analyze popular estimators such as Extended Dynamic Mode Decomposition (EDMD) and Reduced Rank Regression (RRR). Our results rely on novel estimation bounds for operator norm error and a metric distortion functional for estimated eigenfunctions. We uncover insights into the emergence of spurious eigenvalues, addressing an important practical issue. Additionally, by leveraging neural network parameterization, we briefly present a novel approach to learning finite-dimensional RKHS suitable for Koopman operator learning that is intimately linked to deep canonical correlation analysis (CCA). Numerical experiments provide practical illustrations of our findings, highlighting the implications of the developed learning theory.

Overall, this workshop talk aims to bridge the gap between Koopman operator theory and statistical learning, offering guarantees, benefits, and insights while addressing the challenges involved in learning time-homogeneous Markov processes with Koopman operators.

Olteanu, Madalina:

"Feature selection for unsupervised learning"

Assessing the underlying structure of a dataset is often done by training a clustering procedure on the features describing the data. In practice, while the data may be described by a large number of features, only a minority of them may be actually informative with regard to the structure. Furthermore, redundant features may also bias the clustering, whether one speaks of redundancy in the informative or the uninformative features. The first part of this presentation will thus review several approaches for sparse clustering, and focus on two recent algorithms designed for mixed data (made of numerical and categorical features). During the second part of the talk, we will see how the ideas developed for sparse clustering may be transposed in a multivariate change-point detection framework. The performances and the interpretability of the methods will be illustrated on several real-life data sets.

Reynaud-Bouret, Patricia: 

"Neural Coding as a Statistical Testing Problem"

We take the minimax testing perspective to understand what the minimal discrimination time between two stimuli is for different types of rate coding neurons. Our main goal is to describe the testing abilities of two different encoding systems: place cells and grid cells. In particular, we show, through the notion of adaptation, that a fixed place cell system can have a shorter minimum discrimination time when the stimuli are further away. This could be a considerable advantage for the place cell system that could complement the grid cell system, which is able to discriminate stimuli that are much closer than place cells. This is a joint work with Guilherme Ost (Rio de Janeiro)