Does the Wake-sleep Algorithm Produce Good Density Estimators?

The wake-sleep algorithm (Hinton, Dayan, Frey and Neal 1995) is a relatively efficient method of fitting a multilayer stochastic generative model to high-dimensional data. In addition to the top-down connections in the generative model, it makes use of bottom-up connections for approximating the probability distribution over the hidden units given the data, and it trains these bottom-up connections using a simple delta rule. We use a variety of synthetic and real data sets to compare the performance of the wake-sleep algorithm with Monte Carlo and mean field methods for fitting the same generative model and also compare it with other models that are less powerful but easier to fit. 1 INTRODUCTION Neural networks are often used as bottom-up recognition devices that transform input vectors into representations of those vectors in one or more hidden layers. But multilayer networks of stochastic neurons can also be used as top-down generative models that produce patterns with complicated correlational structure in the bottom visible layer. In this paper we consider generative models composed of layers of stochastic binary logistic units. Given a generative model parameterized by top-down weights, there is an obvious way to perform unsupervised learning. The generative weights are adjusted to maximize the probability that the visible vectors generated by the model would match the observed data.