Fast Learning by Bounding Likelihoods in Sigmoid Type Belief Networks

Often the parameters used in these networks needto be learned from examples. Unfortunately, estimating the parameters via exact probabilistic calculations (i.e, the EMalgorithm) is intractable even for networks with fairly small numbers of hidden units. We propose to avoid the infeasibility of the E step by bounding likelihoods instead of computing them exactly. Weintroduce extended and complementary representations for these networks and show that the estimation of the network parameters can be made fast (reduced to quadratic optimization) by performing the estimation in either of the alternative domains. The complementary networks can be used for continuous density estimation as well. 1 Introduction The appeal of probabilistic networks for knowledge representation, inference, and learning (Pearl, 1988) derives both from the sound Bayesian framework and from the explicit representation of dependencies among the network variables which allows readyincorporation of prior information into the design of the network.