MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference

TL;DR

This paper introduces MetFlow, a novel and efficient method that combines Variational Inference with MCMC using flow-based proposals, significantly enhancing expressivity and performance in Bayesian inference tasks.

Contribution

The paper presents MetFlow, a new family of MCMC algorithms utilizing Normalizing Flows, enabling efficient VI-MCMC integration without expensive reverse kernels.

Findings

Demonstrates improved computational efficiency over existing methods

Shows increased expressivity of the variational family with flow-based proposals

Achieves better performance in numerical experiments

Abstract

In this contribution, we propose a new computationally efficient method to combine Variational Inference (VI) with Markov Chain Monte Carlo (MCMC). This approach can be used with generic MCMC kernels, but is especially well suited to \textit{MetFlow}, a novel family of MCMC algorithms we introduce, in which proposals are obtained using Normalizing Flows. The marginal distribution produced by such MCMC algorithms is a mixture of flow-based distributions, thus drastically increasing the expressivity of the variational family. Unlike previous methods following this direction, our approach is amenable to the reparametrization trick and does not rely on computationally expensive reverse kernels. Extensive numerical experiments show clear computational and performance improvements over state-of-the-art methods.