Intracluster Moves for Constrained Discrete-Space MCMC

TL;DR

This paper introduces a novel MCMC algorithm for sampling from constrained binary distributions, enabling large, energetically favorable moves, with applications demonstrated on various Boltzmann machine models.

Contribution

It presents a new MCMC method that efficiently samples from constrained binary spaces, allowing large moves and improved sampling in complex models.

Findings

Effective in sampling from constrained binary distributions

Demonstrated on Ising model, RBM, and spin-glass

Outperforms previous algorithms in move size and efficiency

Abstract

This paper addresses the problem of sampling from binary distributions with constraints. In particular, it proposes an MCMC method to draw samples from a distribution of the set of all states at a specified distance from some reference state. For example, when the reference state is the vector of zeros, the algorithm can draw samples from a binary distribution with a constraint on the number of active variables, say the number of 1's. We motivate the need for this algorithm with examples from statistical physics and probabilistic inference. Unlike previous algorithms proposed to sample from binary distributions with these constraints, the new algorithm allows for large moves in state space and tends to propose them such that they are energetically favourable. The algorithm is demonstrated on three Boltzmann machines of varying difficulty: A ferromagnetic Ising model (with positive potentials), a restricted Boltzmann machine with learned Gabor-like filters as potentials, and a challenging three-dimensional spin-glass (with positive and negative potentials).