MPE inference using an Incremental Build-Infer-Approximate Paradigm

TL;DR

This paper introduces an approximate MPE inference algorithm for Bayesian networks using an incremental build-infer-approximate framework, achieving high accuracy and efficiency without convergence issues.

Contribution

The paper presents a novel incremental framework for approximate MPE inference that guarantees increasing variable assignments and avoids convergence problems.

Findings

Valid assignments in 100 out of 117 benchmarks

Comparable accuracy to branch and bound search

Competitive run times

Abstract

Exact inference of the most probable explanation (MPE) in Bayesian networks is known to be NP-complete. In this paper, we propose an algorithm for approximate MPE inference that is based on the incremental build-infer-approximate (IBIA) framework. We use this framework to obtain an ordered set of partitions of the Bayesian network and the corresponding max-calibrated clique trees. We show that the maximum belief in the last partition gives an estimate of the probability of the MPE assignment. We propose an iterative algorithm for decoding, in which the subset of variables for which an assignment is obtained is guaranteed to increase in every iteration. There are no issues of convergence, and we do not perform a search for solutions. Even though it is a single shot algorithm, we obtain valid assignments in 100 out of the 117 benchmarks used for testing. The accuracy of our solution is comparable to a branch and bound search in majority of the benchmarks, with competitive run times.