The effect of priors on Learning with Restricted Boltzmann Machines
This work addresses the problem of optimizing learning in RBMs for researchers in machine learning, but it is incremental as it builds on existing teacher-student frameworks to analyze prior effects.
The study investigated how priors affect learning efficiency in Restricted Boltzmann Machines (RBMs) using a teacher-student setting, finding that the critical dataset size for generalization depends on teacher properties but not student properties, though student priors can expand the signal retrieval region to facilitate training.
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.