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arXiv · 2205.15902

Variational inference via Wasserstein gradient flows

Marc Lambert·Sinho Chewi·Francis Bach·Silvère Bonnabel·Philippe Rigollet
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Abstract

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.

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Marc Lambert, Sinho Chewi, Francis Bach, Silvère Bonnabel, Philippe Rigollet. 2022-05-31. Variational inference via Wasserstein gradient flows. https://arxiv.org/abs/2205.15902

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