An efficient approach for finding the MPE in belief networks

Given a belief network with evidence, the task of finding the l most probable ex­ planations (MPE) in the belief network is that of identifying and ordering the l most probable instantiations of the non-evidence nodes of the belief network. Although many approaches have been proposed for solving this problem, most work only for restricted topologies (i.e., singly connected belief net­ works). In this paper, we will present a new approach for finding l MPEs in an arbitrary belief network. First, we will present an al­ gorithm for finding the MPE in a belief net­ work. Then, we will present a linear time al­ gorithm for finding the next MPE after find­ ing the first MPE. And finally, we will discuss the problem of finding the MPE for a subset of variables of a belief network, and show that the problem can be efficiently solved by this approach.