On y parlera de graphons, de permutons et du récent papier de Kenyon sur les patterns dans les suites.

On y parlera de divers algorithmes pour faire grossir des arbres binaires uniformes et de leurs limites continues qui sont des diffusions sur l’espace des arbres continus.

Modern statistical learning problems often involve heterogeneous, high-dimensional, or distributed data, raising two complementary challenges: controlling model complexity in high dimensions, and enabling frugal inference under distributional constraints, while preserving both structure and statistical consistency.

In this talk, I present contributions centered on mixture-of-experts (MoE) models, a flexible latent variable framework with well-established approximation capabilities and learning guarantees for conditional densities.

I first consider MoE models with high-dimensional predictors, including functional data such as curves and time series, and their training via Lasso-type regularization in unsupervised settings, enabling sparse and interpretable representations together with non-asymptotic model selection guarantees.

I then address learning from data distributed across multiple sites due to storage, computational, or governance constraints, and present a frugal aggregation strategy for MoE models based on optimal transport, which constructs a reduced global estimator from locally trained models in a single communication round while preserving both model structure and statistical consistency, making it particularly well suited to large-scale settings where communication is a major bottleneck.

Together, these contributions position MoE as a unified framework for principled, interpretable, and scalable statistical learning, with perspectives on frugal learning of generative models at the interface of modern machine learning and AI, and applications in constrained industrial environments.

[exposé en français.]

I will present a construction of the Euclidean sine–Gordon quantum field theory using probabilistic methods. The approach formulates the model through a stochastic control problem and a weak forward–backward stochastic differential equation (FBSDE). The starting point is a detailed study of the perturbation theory associated with the sine–Gordon potential across the full subcritical regime.  For a portion of the subcritical regime extending above 6π, the construction can be made rigorous beyond perturbation theory using a stochastic control problem. I will explain the different regimes of the model and why we currently cannot construct the model in the full subcritical regime.

Queueing systems with a product-form stationary distribution have played a leading role in the development of queueing theory. Popular examples are Jackson networks from the 1950’s, Whittle and BCMP networks from the 1970s, and order-independent queues from the 1990s. The goal of this talk is to give a brief overview of product-form queueing systems. I will first give a short definition, which I will illustrate with several recent applications, namely, to redundancy scheduling and online stochastic matching. In a second time, I will discuss how the form of the stationary distribution can be used to perform inference and optimization in these systems.

Date possible pour le colloquinte