The seminar is normally held on Mondays at 14:00 (2:00 PM CET), room 3001 (3rd floor) of ENSAE building. If you don't work at ENSAE, bring an ID.
The seminar is open; in order to be added to the mailing list, please send an email to Leyla Marzuk (first [dot] last [at] ensae [dot] fr).
Vincent Divol (CREST, ENSAE)
Anna Korba (CREST, ENSAE)
Jaouad Mourtada (CREST, ENSAE)
Monday, September 28, 2:00pm
Michael Jordan (UC Berkeley)
Sequential hypothesis testing is often formulated as the design of stochastic processes that are nonnegative supermartingales under the null hypothesis. Modern challenges in this area involve nonparametric, composite hypotheses, both for the null and the alternative. I present a general theorem delineating a class of nonnegative supermartingales that have optimal power against composite alternatives. The characterization is based on a deterministic quantity known as the "portfolio regret"---I show that any process exhibiting sublinear portfolio regret is adaptively, asymptotically, and almost surely log-optimal. In the second half of the talk I present an application of these ideas to an emerging area at the intersection of statistical inference and economic mechanism design. Specifically, I discuss a game-theoretic problem involving a Principal who wishes to perform tests of hypotheses, where the choice of hypotheses is made by a strategic, self-interested Agent. I show that incentive compatibility in this game is assured if and only if the contract provided by the Principal to the Agent is comprised of a set of nonnegative supermartingales. [Joint work with Stephen Bates, Ricardo Sandoval, Michael Sklar, Jake Soloff, and Ian Waudby-Smith.].
Monday, November 9, 2:00pm
Tim Van Erven (Korteweg-de Vries Institute for Mathematics)
TBA
Monday, September 7, 2:00pm
Kimia Nadjahi (École Normale Supérieure)
Expected Batch Optimal Transport Plans and Consequences for Flow Matching
Solving optimal transport (OT) on random minibatches is a common surrogate for exact OT in large-scale learning. In flow matching (FM), this surrogate is used to obtain OT-like couplings that can straighten probability paths and reduce numerical integration cost. Yet, the population-level coupling induced by repeated minibatch OT remains only partially understood. We formalize this coupling as the expected batch OT plan, obtained by averaging empirical OT plans over independent minibatches. We then establish its large-batch consistency and, in the semidiscrete case relevant to generative modeling, derive rates for both the transport-cost bias and the convergence of the expected batch OT plan to the OT plan. For FM, this yields a population coupling whose induced velocity field is regular enough to define a unique flow from the source to the discrete target. We finally quantify how OT batch size interacts with numerical integration in a tractable two-atom model and in synthetic and image experiments.
Monday, September 14, 2:00pm
Richard Nickl (University of Cambridge)
Statistical Inference for infinite-dimensional dynamical systems
We study optimal statistical inference procedures for the states of time evolution phenomena occurring in `data assimilation’ or filtering problems. There it is a common practice to assign a Gaussian process prior on the initial condition of a dynamical system and to update it to a Bayesian posterior measure in the space of possible trajectories given a discrete sample of the process. In key applications the dynamics are non-linear, such as with Navier-Stokes equations in geophysical sciences or reaction-diffusion equations in biochemistry. While Bayesian posterior distributions are widely computed by filtering or MCMC methods, little is known about the statistical behaviour of these posterior measures in non-linear settings. In this talk we will introduce a theoretical framework for such models and then present recent results, known as `Bernstein-von Mises theorems’, that show that the posterior measures are approximated in function space by the Gaussian laws of solutions to certain SPDEs that involve the inverse Fisher information of the underlying statistical model.
Monday, September 21, 2:00pm
David Ginsbourger (University of Bern)
The Many Lives of Gaussian Processes
Beyond their foundational roots in statistical and stochastic process theory, Gaussian processes (GPs) are now central to a versatile and widely used framework spanning applied mathematics and probabilistic machine learning. Despite well-known limitations, GP-based methods continue to show remarkable adaptability, often outlasting shifting methodological trends. In this talk, I will highlight developments in modeling, prediction, and active learning with GPs, offering perspectives on their enduring role as a powerful building block for function approximation and uncertainty quantification.