cient 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 nding one or more of the most probable instantiations of a network In this paper we develop an e cient 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