Membres | CEREMADE - UMR CNRS 7534 - Université Paris-Dauphine

Séminaire

Rencontres statistiques

OCELLO Antonio (Polytechnique)

Le 31/03/2025
De 13:30 à 14:30
Titre : Theoretical Advances in Score-Based Generative Models: Convergence Bounds and Noise Schedule Optimization

Résumé : Score-based generative models (SGMs) have emerged as a state-of-the-art framework for sampling from complex data distributions, leveraging the estimation of score functions through noise-perturbed samples. A central challenge in understanding SGMs lies in quantifying their convergence to the target distribution. Various works have analyzed this convergence using Kullback-Leibler (KL) divergence and Wasserstein distances, often under restrictive assumptions.In this talk, I will present an overview of existing convergence bounds for SGMs and introduce two recent contributions that provide a refined theoretical understanding of their performance. First, I will discuss our work on the impact of the noise schedule on generative performance, where we establish explicit upper bounds for the KL divergence and Wasserstein-2 distance under mild assumptions. This result not only improves upon prior state-of-the-art bounds but also provides practical insights into hyperparameter selection. Building on this framework, I will then present recent advances in Wasserstein-2 convergence analysis. By leveraging the regularization properties of the Ornstein–Uhlenbeck (OU) process, we relax the traditional assumptions of log-concavity and score regularity. Our approach reveals that weakly log-concave distributions evolve towards log-concavity, and we establish a novel characterization of the dynamics of score function contraction and non-contraction. This enables more general and widely applicable convergence results, particularly for complex distributions such as Gaussian mixtures. This talk is based on joint work with Stanislas Strasman, Claire Boyer, Sylvain Le Corff, and Vincent Lemaire, recently accepted to Transactions on Machine Learning Research (https://openreview.net/forum?id=BlYIPa0Fx1), as well as a recent preprint in collaboration with Marta Gentiloni-Silveri (https://arxiv.org/abs/2501.02298).

Salle : A711

Colloque

Colloquium du CEREMADE

REYNAUD-BOURET Patricia (Université Côte d'Azur)

Le 01/04/2025
De 15:30 à 16:30
Titre : Kalikow decomposition for the study of neuronal networks: simulation and learning

Résumé : Kalikow decomposition is a decomposition of stochastic processes (usually finite state discrete time processes but also more recently point processes) that consists in picking at random a finite neighborhood in the past and then make a transition in a Markov manner. This kind of approach has been used for many years to prove existence of some processes, especially their stationary distribution. In particular, it allows to prove the existence of processes that model infinite neuronal networks, such as Hawkes like processes or Galvès-Löcherbach processes. But beyond mere existence, this decomposition is a wonderful tool to simulate such network, as an open physical system, that from a computational point of view could be competitive with the most performant brain simulations. This decomposition is also a source of inspiration to understand how local rules at each neuron can make the whole network learn.

Salle : A709

Séminaire

Séminaire des jeunes chercheurs

LEBLANC Théo (CEREMADE)

Le 03/04/2025
De 17:00 à 18:00
Titre : Hawkes and Autoregressive processes in Neuroscience

Résumé : In this talk we present a special class of point processes: Hawkes processes and focus on how Hawkes processes can be used in Mathematical Neuroscience to model functional connectivity. In neuroscience, functional connectivity can be seen as an ensemble of interactions between brain oscillations (rhythms) and individual neuronal activity (spikes). Neuronal activity can be modeled by a multivariate Hawkes process. The points of the Hawkes process correspond to the spiking times of each neurons and the spiking activity at time t depends on past spikes of the different neurons. Brain rhythms, another important quantity about brain activity, can be defined as the wavelet coefficients of the LFP (local field potential) signals and are therefore treated as discrete sequences. Autoregressive equations are the standard way of modeling interactions between brain rhythms. We introduce a coupled model combining both Hawkes and AutoRegressive processes to describe at once all possible interactions between neurons and brain rhythms. We present theoretical results and a statistical method based on the LASSO to infer functional connectivity.

Salle : A707

Séminaire

Rencontres statistiques

GUEDON Tom (INRAE)

Le 07/04/2025
De 16:00 à 17:00
Titre : Estimation de ratio de constante de normalisation: l'algorithme SARIS.

Résumé : Le calcul des rapports de constante de normalisation joue un rôle important dans la modélisation statistique. Deux exemples notables sont les tests d’hypothèses dans les modèles à variables latentes et la comparaison de modèles en statistique bayésienne. Dans ces deux cas, le rapport de vraisemblance et le facteur de Bayes sont définis comme le rapport des constantes de normalisation des distributions a posteriori. Nous proposons dans cet article une nouvelle méthodologie qui estime ce rapport en utilisant le principe de l’approximation stochastique. Notre estimateur est consistant et asymptotiquement gaussien. Sa variance asymptotique est plus faible que celle de l’estimateur populaire bridge sampling. En outre, il est beaucoup plus robuste lorsque les supports des deux distributions non normalisées considérées se chevauchent peu. Grâce à sa définition en ligne, notre procédure peut être intégrée dans un processus d'estimation dans les modèles à variables latentes, ce qui permet ainsi de réduire l’effort de calcul. Les performances de l’estimateur sont illustrées par une étude de simulation et comparées à celles de deux autres estimateurs : le ratio importance sampling et le bridge sampling.

Salle : B315

Séminaire