Approximating MAP using Local Search

TL;DR

This paper introduces a local search method for approximating MAP in Bayesian networks, significantly reducing complexity and improving accuracy over existing approximation techniques.

Contribution

The paper presents a novel local search approach for MAP approximation that is more efficient and accurate than previous methods, with complexity tied to treewidth.

Findings

Local search yields more accurate MAP approximations.

The method requires fewer search steps for effective results.

Complexity is exponential only in treewidth, not constrained treewidth.

Abstract

MAP is the problem of finding a most probable instantiation of a set of variables in a Bayesian network, given evidence. Unlike computing marginals, posteriors, and MPE (a special case of MAP), the time and space complexity of MAP is not only exponential in the network treewidth, but also in a larger parameter known as the "constrained" treewidth. In practice, this means that computing MAP can be orders of magnitude more expensive than computingposteriors or MPE. Thus, practitioners generally avoid MAP computations, resorting instead to approximating them by the most likely value for each MAP variableseparately, or by MPE.We present a method for approximating MAP using local search. This method has space complexity which is exponential onlyin the treewidth, as is the complexity of each search step. We investigate the effectiveness of different local searchmethods and several initialization strategies and compare them to otherapproximation schemes.Experimental results show that local search provides a much more accurate approximation of MAP, while requiring few search steps.Practically, this means that the complexity of local search is often exponential only in treewidth as opposed to the constrained treewidth, making approximating MAP as efficient as other computations.