The new season of mostly Monte Carlo has started with three talks this very Friday! At Paris Santé Campus as usual.
14h El Mahdi Khribch (ESSEC)
Contributions to the Theory of Bayesian Computation: Bias, Information, and Robustness.
Abstract: Bayesian inference is rarely computable exactly, and every practical substitute, whether a Monte Carlo sampler, a tempered posterior or a variational approximation, carries an error. This thesis gives finite-sample guarantees for three of them: the bias of sampling-based integration, the information cost of data-dependent posteriors, and the robustness of inference under misspecification. The unifying tools throughout are PAC-Bayesian change-of-measure inequalities and their information-theoretic counterparts.
15h Federica Milinanni (Northwestern University)
Rapid Mixing of Stereographic MCMC for Heavy-Tailed Sampling
Abstract: Sampling from high-dimensional, heavy-tailed distributions is a fundamental challenge in computational statistics, as many standard Markov chain Monte Carlo (MCMC) methods mix poorly in such settings. Recently, Stereographic MCMC [Yang et al., 2024] and the Sub-Cauchy Projection Sampler [Grazzi et al., 2026] have been shown to perform successfully on such tasks. However, establishing their non-asymptotic convergence properties remains an important open problem. In this work, we fill this gap by establishing non-asymptotic upper bounds on the mixing time of the stereographic projection and sub-Cauchy projection samplers. Our results demonstrate that, under certain conditions on the target and initial distributions, the mixing time is polynomial in dimension for a broad class of distributions, including light- and heavy-tailed cases.
Motivated by the theoretical analysis, we further establish a new weighted isoperimetric inequality that extends the classical version for (strongly) log-concave distributions to the heavy-tailed setting with optimal dimension dependence.
The proof techniques provide new insights into the geometric properties of heavy-tailed distributions that govern rapid mixing in high dimensions.
This is joint work with Tyler Farghly (Inria) and Jun Yang (University of Copenhagen)
16h Sylvain Procope-Mamert (INRAe)
A forward only method to construct proposal distributions in particle filters
Abstract: Particle filters are powerful algorithms used to sample from a sequence of distributions. It is useful notably, for Bayesian inference with different types of models and real data applications. In particular, when we try to recover a hidden signal from sequentially produced data with state-space models, the canonically defined proposals known as the bootstrap particle filter are rarely well-behaved and need extra work to be turned into useful sampling algorithms. Previous works on iterated methods for the automated construction of sequential Monte Carlo proposals, which were based on a backward scheme, have shown how to gradually improve proposals to reach a global optimality criterion, but they require a good initial proposal and cannot be used online.
