Variational inference via Wasserstein gradient flows

arXiv2205.15902MaRDI QIDQ6400705

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Publication date: 31 May 2022

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 $hatpi$ 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 $hatpi$ 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.

Has companion code repository: https://github.com/marc-h-lambert/w-vi

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