Variational inference via Wasserstein gradient flows
Marc Lambert, Sinho Chewi, Francis Bach, Silvère Bonnabel, Philippe Rigollet
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.
BibTeX
@inproceedings{
lambert2022variational,
title={Variational inference via Wasserstein gradient flows},
author={Marc Lambert and Sinho Chewi and Francis Bach and Silv{\`e}re Bonnabel and Philippe Rigollet},
booktitle={Advances in Neural Information Processing Systems},
editor={Alice H. Oh and Alekh Agarwal and Danielle Belgrave and Kyunghyun Cho},
year={2022},
url={https://openreview.net/forum?id=K2PTuvVTF1L}
}