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Variational inference via Wasserstein gradient flows
Marc Lambert · Sinho Chewi · Francis Bach · Silvère Bonnabel · Philippe Rigollet

Thu Dec 01 02:00 PM -- 04:00 PM (PST) @ Hall J #726
Along with Markov chain Monte Carlo (MCMC) methods, variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. Rather than sampling from the true posterior $\pi$, VI aims at producing a simple but effective approximation $\hat \pi$ to $\pi$ for which summary statistics are easy to compute. However, unlike the well-studied MCMC methodology, algorithmic guarantees for VI are still relatively less well-understood. In this work, we propose principled methods for VI, in which $\hat \pi$ is taken to be a Gaussian or a mixture of Gaussians, which rest upon the theory of gradient flows on the Bures--Wasserstein space of Gaussian measures. Akin to MCMC, it comes with strong theoretical guarantees when $\pi$ is log-concave.

Author Information

Marc Lambert (INRIA)
Sinho Chewi (Massachusetts Institute of Technology)
Francis Bach (INRIA - Ecole Normale Superieure)

Francis Bach is a researcher at INRIA, leading since 2011 the SIERRA project-team, which is part of the Computer Science Department at Ecole Normale Supérieure in Paris, France. After completing his Ph.D. in Computer Science at U.C. Berkeley, he spent two years at Ecole des Mines, and joined INRIA and Ecole Normale Supérieure in 2007. He is interested in statistical machine learning, and especially in convex optimization, combinatorial optimization, sparse methods, kernel-based learning, vision and signal processing. He gave numerous courses on optimization in the last few years in summer schools. He has been program co-chair for the International Conference on Machine Learning in 2015.

Silvère Bonnabel
Philippe Rigollet (MIT)

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