LSB: Local Self-Balancing MCMC in Discrete Spaces

TL;DR

The paper introduces LSB, a novel local MCMC sampler for discrete spaces that adaptively reduces target evaluations by balancing proposals through mutual information-based objectives and self-learning.

Contribution

The paper proposes LSB, a self-balancing local MCMC method with a new objective function for efficient sampling in discrete domains, outperforming existing local samplers.

Findings

LSB converges with fewer oracle queries than recent local MCMC methods.

LSB adapts autonomously to the target distribution.

Experimental results on energy-based models demonstrate improved efficiency.

Abstract

We present the Local Self-Balancing sampler (LSB), a local Markov Chain Monte Carlo (MCMC) method for sampling in purely discrete domains, which is able to autonomously adapt to the target distribution and to reduce the number of target evaluations required to converge. LSB is based on (i) a parametrization of locally balanced proposals, (ii) a newly proposed objective function based on mutual information and (iii) a self-balancing learning procedure, which minimises the proposed objective to update the proposal parameters. Experiments on energy-based models and Markov networks show that LSB converges using a smaller number of queries to the oracle distribution compared to recent local MCMC samplers.