Constructing the dependency structure of a multiagent probabilistic network

A probabilistic network consists of a dependency structure and corresponding probability tables. The dependency structure is a graphical representation of the conditional independencies that are known to hold in the problem domain. We propose an automated process for constructing the combined dependency structure of a multiagent probabilistic network. Each domain expert supplies any known conditional independency information and not necessarily an explicit dependency structure. Our method determines a succinct representation of all the supplied independency information called a minimal cover. This process involves detecting all inconsistent information and removing all redundant information. A unique dependency structure of the multiagent probabilistic network can be constructed directly from this minimal cover. The main result is that the constructed dependency structure is a perfect-map of the minimal cover. That is, every probabilistic conditional independency logically implied by the minimal cover can be inferred from the dependency structure and every probabilistic conditional independency inferred from the dependency structure is logically implied by the minimal cover.