Revising Bayesian Network Parameters Using Backpropagation

The problem of learning Bayesian networks with hidden variables is known to be a hard problem. Even the simpler task of learning just the conditional probabilities on a Bayesian network with hidden variables is hard. In this paper, we present an approach that learns the conditional probabilities on a Bayesian network with hidden variables by transforming it into a multi-layer feedforward neural network (ANN). The conditional probabilities are mapped onto weights in the ANN, which are then learned using standard backpropagation techniques. Toavoid the problem of exponentially large ANNs, we focus on Bayesian networks with noisy-or and noisyand nodes. Experiments on real world classi cation problems demonstrate the e ectiveness of our technique. 1

Learning Qualitative Models for Systems with Multiple Operating Regions*

The problem of learning qualitative models of physical systems from observations of its behaviour has been addressed by several researchers in recent years. Most current techniques limit themselves to learning a single qualitative differential equation to model the entire systeni. However, many systems have several qualitative differential equations underlying thenm. In this paper, we present arm approach to learning the models for such systems. Our technique divides the belmaviours into segments, each of which can be explained by a single qualitative differential eqima— tion. The qualitative model for each segment cami be generated using any of the existing techniques for learning a single model. We show the results of applying our technique to several examples and demonstrate that it is effective