Speeding up approximate MAP by applying domain knowledge about relevant variables

TL;DR

This paper investigates whether incorporating domain knowledge about relevant variables can accelerate approximate MAP inference in Bayesian networks, comparing its performance against exact and approximate methods.

Contribution

It explores the potential of using domain knowledge to identify relevant variables, aiming to improve the efficiency of approximate MAP algorithms.

Findings

Results are inconclusive regarding speed improvements.

Effectiveness depends on the number of MAP variables.

Domain knowledge may influence computational efficiency.

Abstract

The MAP problem in Bayesian networks is notoriously intractable, even when approximated. In an earlier paper we introduced the Most Frugal Explanation heuristic approach to solving MAP, by partitioning the set of intermediate variables (neither observed nor part of the MAP variables) into a set of relevant variables, which are marginalized out, and irrelevant variables, which will be assigned a sampled value from their domain. In this study we explore whether knowledge about which variables are relevant for a particular query (i.e., domain knowledge) speeds up computation sufficiently to beat both exact MAP as well as approximate MAP while giving reasonably accurate results. Our results are inconclusive, but also show that this probably depends on the specifics of the MAP query, most prominently the number of MAP variables.