An efficient approach for finding the MPE in belief networks

TL;DR

This paper introduces a new efficient method for identifying the most probable explanations in any belief network, regardless of its topology, improving over previous restricted approaches.

Contribution

It presents a novel algorithm for finding the MPE in arbitrary belief networks and a linear-time method for subsequent MPEs, extending applicability beyond singly connected networks.

Findings

The algorithm efficiently finds the MPE in general belief networks.

A linear-time algorithm for subsequent MPEs is proposed.

The approach can handle MPEs for variable subsets within belief networks.

Abstract

Given a belief network with evidence, the task of finding the I most probable explanations (MPE) in the belief network is that of identifying and ordering the I 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 networks). In this paper, we will present a new approach for finding I MPEs in an arbitrary belief network. First, we will present an algorithm for finding the MPE in a belief network. Then, we will present a linear time algorithm for finding the next MPE after finding 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.