Learning a Restricted Boltzmann Machine using biased Monte Carlo sampling

TL;DR

This paper introduces a biased Monte Carlo sampling method, Tethered Monte Carlo, to accelerate sampling and training of Restricted Boltzmann Machines, especially on low-dimensional clustered datasets, improving efficiency and model quality.

Contribution

The paper demonstrates that Tethered Monte Carlo can significantly speed up RBM training and sampling by overcoming phase coexistence issues, a novel application in this context.

Findings

TMC accelerates sampling in RBMs with clustered datasets.

TMC improves the computation of log-likelihood gradients during training.

TMC enables recovery of the RBM free-energy profile.

Abstract

Restricted Boltzmann Machines are simple and powerful generative models that can encode any complex dataset. Despite all their advantages, in practice the trainings are often unstable and it is difficult to assess their quality because the dynamics are affected by extremely slow time dependencies. This situation becomes critical when dealing with low-dimensional clustered datasets, where the time required to sample ergodically the trained models becomes computationally prohibitive. In this work, we show that this divergence of Monte Carlo mixing times is related to a phenomenon of phase coexistence, similar to that which occurs in physics near a first-order phase transition. We show that sampling the equilibrium distribution using the Markov chain Monte Carlo method can be dramatically accelerated when using biased sampling techniques, in particular the Tethered Monte Carlo (TMC) method. This sampling technique efficiently solves the problem of evaluating the quality of a given trained model and generating new samples in a reasonable amount of time. Moreover, we show that this sampling technique can also be used to improve the computation of the log-likelihood gradient during training, leading to dramatic improvements in training RBMs with artificial clustered datasets. On real low-dimensional datasets, this new training method fits RBM models with significantly faster relaxation dynamics than those obtained with standard PCD recipes. We also show that TMC sampling can be used to recover the free-energy profile of the RBM. This proves to be extremely useful to compute the probability distribution of a given model and to improve the generation of new decorrelated samples in slow PCD-trained models.