Training Products of Experts by Minimizing Contrastive Divergence

TLDR

Combining latent‑variable models by multiplying their distributions yields a product of experts that is easy to infer but difficult to sample. The authors propose using a product of experts as a perceptual system where fast inference is essential and generation is not required. They train the product of experts with contrastive divergence, which provides accurate and efficient parameter gradients despite the intractable renormalization term. Experiments demonstrate contrastive divergence learning on several expert types and data sets.

Abstract

It is possible to combine multiple latent-variable models of the same data by multiplying their probability distributions together and then renormalizing. This way of combining individual "expert" models makes it hard to generate samples from the combined model but easy to infer the values of the latent variables of each expert, because the combination rule ensures that the latent variables of different experts are conditionally independent when given the data. A product of experts (PoE) is therefore an interesting candidate for a perceptual system in which rapid inference is vital and generation is unnecessary. Training a PoE by maximizing the likelihood of the data is difficult because it is hard even to approximate the derivatives of the renormalization term in the combination rule. Fortunately, a PoE can be trained using a different objective function called "contrastive divergence" whose derivatives with regard to the parameters can be approximated accurately and efficiently. Examples are presented of contrastive divergence learning using several types of expert on several types of data.