A Langevin-like Sampler for Discrete Distributions

TL;DR

This paper introduces a discrete Langevin proposal (DLP), a gradient-based method for efficiently sampling high-dimensional discrete distributions, outperforming existing methods in various complex models.

Contribution

The paper presents DLP, a scalable, parallelizable discrete sampling method with theoretical efficiency guarantees and multiple variants, improving over traditional Gibbs sampling.

Findings

DLP achieves zero asymptotic bias for log-quadratic distributions.

DLP outperforms popular sampling methods on models like Ising, RBMs, and neural networks.

Various DLP variants demonstrate versatility and efficiency in high-dimensional discrete sampling.

Abstract

We propose discrete Langevin proposal (DLP), a simple and scalable gradient-based proposal for sampling complex high-dimensional discrete distributions. In contrast to Gibbs sampling-based methods, DLP is able to update all coordinates in parallel in a single step and the magnitude of changes is controlled by a stepsize. This allows a cheap and efficient exploration in the space of high-dimensional and strongly correlated variables. We prove the efficiency of DLP by showing that the asymptotic bias of its stationary distribution is zero for log-quadratic distributions, and is small for distributions that are close to being log-quadratic. With DLP, we develop several variants of sampling algorithms, including unadjusted, Metropolis-adjusted, stochastic and preconditioned versions. DLP outperforms many popular alternatives on a wide variety of tasks, including Ising models, restricted Boltzmann machines, deep energy-based models, binary neural networks and language generation.