Geoffrey E. Hinton, Dept. of Computer Science, University of Toronto

Radford M. Neal, Dept. of Computer Science, University of Toronto

Richard S. Zemel, The Salk Institute

Discovering the structure inherent in a set of patterns is a fundamental aim of statistical inference or learning. One fruitful approach is to build a parameterised stochastic generative model, independent draws from which are likely to produce the patterns. For all but the simplest generative models, each pattern can be generated in exponentially many ways. It is thus intractable to adjust the parameters to maximize the probability of the observed patterns, We describe a way of finessing this combinatorial explosion by maximising an easily computed lower bound on the probability of the observations. Our method can be viewed as a form of hierarchical self-supervised learning that may relate to the function of bottom-up and top-down cortical processing pathways.

*Neural Computation*, vol. 7, pp. 1022-1037 (1995).

Hinton, G. E., Dayan, P., Frey, B. J., and Neal, R. M. (1995) ``The ``wake-sleep'' algorithm for unsupervised neural networks'',Science, vol. 268, pp. 1158-1161: abstract, associated references.