From Monte Carlo to Las Vegas: Improving Restricted Boltzmann Machine Training Through Stopping Sets

TL;DR

This paper introduces Markov Chain Las Vegas (MCLV), a new estimator for RBM training that provides statistical guarantees and outperforms traditional Contrastive Divergence methods on MNIST.

Contribution

The paper proposes MCLV, a Las Vegas transformation of MCMC estimators for RBMs, offering guaranteed convergence and improved training performance.

Findings

MCLV-K outperforms CD-K in RBM training on MNIST.

MCLV provides statistical guarantees with random running times.

LVS-K demonstrates significant improvements over traditional methods.

Abstract

We propose a Las Vegas transformation of Markov Chain Monte Carlo (MCMC) estimators of Restricted Boltzmann Machines (RBMs). We denote our approach Markov Chain Las Vegas (MCLV). MCLV gives statistical guarantees in exchange for random running times. MCLV uses a stopping set built from the training data and has maximum number of Markov chain steps K (referred as MCLV-K). We present a MCLV-K gradient estimator (LVS-K) for RBMs and explore the correspondence and differences between LVS-K and Contrastive Divergence (CD-K), with LVS-K significantly outperforming CD-K training RBMs over the MNIST dataset, indicating MCLV to be a promising direction in learning generative models.