Efficient enumeration of instantiations in Bayesian networks

Over the past several years Bayesian net­ works have been applied to a wide variety of problems. A central problem in applying Bayesian networks is that of finding one or more of the most probable instantiations of a network. In this paper we develop an efficient algorithm that incrementally enumerates the instantiations of a Bayesian network in de­ creasing order of probability. Such enumer­ ation algorithms are applicable in a variety of applications ranging from medical expert systems to model-based diagnosis. Funda­ mentally, our algorithm is simply performing a lazy enumeration of the sorted list of all instantiations of the network. This insight leads to a very concise algorithm statement which is both easily understood and imple­ mented. We show that for singly connected networks, our algorithm generates the next instantiation in time polynomial in the size of the network. The algorithm extends to arbi­ trary Bayesian networks using standard con­ ditioning techniques. We empirically evalu­ ate the enumeration algorithm and demon­ strate its practicality.