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Philippe Rigollet (MIT) – “Variational inference via Wasserstein gradient flows”
Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 9th of May 2022
Place: Amphi 200
Philippe RIGOLLET (MIT) – “Variational inference via Wasserstein gradient flows”
Abstract: Bayesian methodology typically generates a high-dimensional posterior distribution that is known only up to normalizing constants, making the computation even of simple summary statistics such as mean and covariance a major computational hurdle. Along with Monte Carlo Markov Chains (MCMC), Variational Inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior, VI aims at producing a simple but good approximation of the target posterior for which summary statistics are easy to compute. However, unlike MCMC theory, which is well-developed and builds on now-classical probabilistic ideas, VI is still poorly understood and dominated by heuristics. In this work, we propose a principled method for VI that builds upon the theory of gradient flows on the Bures-Wasserstein space of Gaussian measures. Akin to MCMC, it comes with theoretical guarantees when the target measure is strongly log-concave.
This joint work with Francis Bach, Silvère Bonnabel, Sinho Chewi, and Marc Lambert.
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)