## Variational inference via Wasserstein gradient flows

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

##### Hall J #726

Keywords: [ Kalman filter ] [ mixture of Gaussians ] [ Wasserstein gradient flow ] [ Bures-Wasserstein ] [ Variational Inference ]

[ Abstract ]
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Thu 1 Dec 2 p.m. PST — 4 p.m. PST

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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