A knowledge representation scheme for the Bayesian network model

The Bayesian network model forms the basis for probabilistic reasoning in this exposition. A Bayesian network consists of a directed acyclic graph, and a set of conditional probability tables. The directed acyclic graph encodes the conditional independencies of the domain variables. The product of the conditional probability tables defines a joint probability distribution representing the domain knowledge. In order to build a Bayesian network, one may construct the directed acyclic graph based on the causal relationships of the variables involved. However, in many applications it may be necessary to construct the directed acyclic graph from the conditional independency information supplied by the experts.; This thesis suggests a hierarchical characterization of input conditional independencies that can be faithfully represented by a Bayesian network. This characterization leads to an alternative representation of Bayesian networks. Methods have been developed to construct suitable hierarchical covers for an input set of conditional independencies. These covers can be represented by an alternative graphical structure defined by a hierarchical set of acyclic hypergraphs. Probabilistic inference can be directly performed using these hypergraphs without the need to first convert them into a secondary structure as in conventional Bayesian networks. Moreover, a method is suggested to compute the marginals of the proposed representation such that all the input independency information is preserved for probabilistic reasoning.