The effect of priors on Learning with Restricted Boltzmann Machines

TL;DR

This paper investigates how different priors in Restricted Boltzmann Machines affect learning efficiency and generalization, revealing a critical dataset size and how priors influence training and signal retrieval.

Contribution

It introduces a parametric class of priors interpolating between Gaussian and binary variables, analyzing their impact on RBM learning in teacher-student setups.

Findings

Existence of a critical dataset size for learning

Prudent prior choices expand the signal retrieval region

Critical size depends on teacher properties, not student priors

Abstract

Restricted Boltzmann Machines (RBMs) are generative models designed to learn from data with a rich underlying structure. In this work, we explore a teacher-student setting where a student RBM learns from examples generated by a teacher RBM, with a focus on the effect of the unit priors on learning efficiency. We consider a parametric class of priors that interpolate between continuous (Gaussian) and binary variables. This approach models various possible choices of visible units, hidden units, and weights for both the teacher and student RBMs. By analyzing the phase diagram of the posterior distribution in both the Bayes optimal and mismatched regimes, we demonstrate the existence of a triple point that defines the critical dataset size necessary for learning through generalization. The critical size is strongly influenced by the properties of the teacher, and thus the data, but is unaffected by the properties of the student RBM. Nevertheless, a prudent choice of student priors can facilitate training by expanding the so-called signal retrieval region, where the machine generalizes effectively.