Properties and Bayesian fitting of restricted Boltzmann machines

TL;DR

This paper explores the properties of restricted Boltzmann machines (RBMs), their challenges in likelihood-based inference, and discusses Bayesian methods for fitting these models to better understand their behavior and uncertainty quantification.

Contribution

It provides a detailed analysis of RBM properties, discusses inference difficulties, and proposes Bayesian approaches for model fitting and uncertainty assessment.

Findings

RBMs can exhibit degeneracy and instability.

Likelihood-based inference faces significant challenges.

Bayesian methods offer a promising alternative for RBM fitting.

Abstract

A restricted Boltzmann machine (RBM) is an undirected graphical model constructed for discrete or continuous random variables, with two layers, one hidden and one visible, and no conditional dependency within a layer. In recent years, RBMs have risen to prominence due to their connection to deep learning. By treating a hidden layer of one RBM as the visible layer in a second RBM, a deep architecture can be created. RBMs are thought to thereby have the ability to encode very complex and rich structures in data, making them attractive for supervised learning. However, the generative behavior of RBMs is largely unexplored and typical fitting methodology does not easily allow for uncertainty quantification in addition to point estimates. In this paper, we discuss the relationship between RBM parameter specification in the binary case and model properties such as degeneracy, instability and uninterpretability. We also describe the associated difficulties that can arise with likelihood-based inference and further discuss the potential Bayes fitting of such (highly flexible) models, especially as Gibbs sampling (quasi-Bayes) methods are often advocated for the RBM model structure.