Structured Probabilistic Neural Networks

Probabilistic inference networks capture the stochastic relation between variables by ‘directed’ probabilistic rules corresponding to conditional probabilities, e.g. p(Ak|Ai∧Aj). Associative neural networks – like Boltzmann machine networks – yield a joint distribution, which is a special case of the distribution generated by inference networks. In this paper conventional associative neural networks with bivariate links and hidden units are systematically extended to the structural form of probabilistic inference networks. The maximum likelihood method is used to combine different, possibly conflicting sets of data yielding appropriate learning algorithms. This allows the integration of associative relations with directed probabilistic rules in a single network, which – in contrast to usual probabilistic inference networks – may contain hidden units. Learning procedures for asymmetric connections are a novel feature and allow the training of networks with a variety of structural properties.