Feature pooling in a Bayesian network with noisy-OR and noisy-AND gates

Abstract

Bayesian network is a promising model of cerebral cortex. However, in ordinary Bayesian networks, the number of parameters increases exponentially against the number of parent nodes in each conditional probability table (CPT), which prohibits employing a large-scale Bayesian network. Restricting CPTs is an approach for scaling-up Bayesian networks. In this paper, we restrict CPTs to noisy-OR and noisy-AND gates, both of which have O(N) parameters against the number of parent nodes N. In order to investigate the representational power of this Bayesian network, we construct a network which can pool the features of the input data, by mimicking the early visual cortex. In this model, a gating mechanism is realized by the noisy-AND gates. We show that the model can acquire translation-invariant responses by the standard gradient ascent method.