September
This seminar is scheduled for 2PM.
Contributions to the Theory of Bayesian Computation: Bias, Information, and Robustness
Mehdi Khribch ESSEC Business School
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.
Rapid Mixing of Stereographic MCMC for Heavy-Tailed Sampling
Federica Milinanni Northwestern University
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)
A forward only method to construct proposal distributions in particle filters
Sylvain Procope-Mamert INRAE
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.