MetFlow: A New Efficient Method for Bridging the Gap between Markov Chain Monte Carlo and Variational Inference
This addresses the efficiency gap between MCMC and VI for probabilistic inference, offering a novel hybrid approach with practical benefits.
The paper tackles the problem of bridging Markov Chain Monte Carlo (MCMC) and Variational Inference (VI) by proposing MetFlow, a method that uses Normalizing Flows to enhance expressivity, resulting in clear computational and performance improvements over state-of-the-art methods.
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.