Sampling in Combinatorial Spaces with SurVAE Flow Augmented MCMC

TL;DR

This paper introduces a novel MCMC sampling method for discrete spaces by combining neural transport techniques with the Metropolis-Hastings rule, enabling efficient sampling where traditional HMC fails.

Contribution

It presents a new approach that uses SurVAE Flows to enable MCMC sampling in discrete domains through continuous embeddings and learned transformations.

Findings

Improved sampling efficiency over existing algorithms.

Effective in diverse applications like statistics, physics, and machine learning.

Demonstrated success in complex discrete distribution sampling.

Abstract

Hybrid Monte Carlo is a powerful Markov Chain Monte Carlo method for sampling from complex continuous distributions. However, a major limitation of HMC is its inability to be applied to discrete domains due to the lack of gradient signal. In this work, we introduce a new approach based on augmenting Monte Carlo methods with SurVAE Flows to sample from discrete distributions using a combination of neural transport methods like normalizing flows and variational dequantization, and the Metropolis-Hastings rule. Our method first learns a continuous embedding of the discrete space using a surjective map and subsequently learns a bijective transformation from the continuous space to an approximately Gaussian distributed latent variable. Sampling proceeds by simulating MCMC chains in the latent space and mapping these samples to the target discrete space via the learned transformations. We demonstrate the efficacy of our algorithm on a range of examples from statistics, computational physics and machine learning, and observe improvements compared to alternative algorithms.