Variational inference via Wasserstein gradient flows

• URL: http://arxiv.org/abs/2205.15902v3
• Date: Fri, 21 Apr 2023 16:33:14 GMT
• Title: Variational inference via Wasserstein gradient flows
• Authors: Marc Lambert, Sinho Chewi, Francis Bach, Silv\`ere Bonnabel, Philippe Rigollet
• Abstract summary: variational inference (VI) has emerged as a central computational approach to large-scale Bayesian inference. We propose principled methods for VI, in which $hat pi$ is taken to be a Gaussian or a mixture of Gaussians.
• Score: 10.039378223592013
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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