Annealed MAP

TL;DR

The paper introduces AnnealedMAP, a simulated annealing-based algorithm for solving the NP-hard MAP problem in Bayesian networks, capable of handling large, complex networks more effectively than previous methods.

Contribution

It presents a novel annealed simulated annealing algorithm for MAP inference, improving solution quality and scalability in complex Bayesian networks.

Findings

Successfully solves large Bayesian networks beyond previous methods' reach.

Maintains high-quality MAP solutions in complex networks.

Outperforms existing approaches in scalability and solution quality.

Abstract

Maximum a Posteriori assignment (MAP) is the problem of finding the most probable instantiation of a set of variables given the partial evidence on the other variables in a Bayesian network. MAP has been shown to be a NP-hard problem [22], even for constrained networks, such as polytrees [18]. Hence, previous approaches often fail to yield any results for MAP problems in large complex Bayesian networks. To address this problem, we propose AnnealedMAP algorithm, a simulated annealing-based MAP algorithm. The AnnealedMAP algorithm simulates a non-homogeneous Markov chain whose invariant function is a probability density that concentrates itself on the modes of the target density. We tested this algorithm on several real Bayesian networks. The results show that, while maintaining good quality of the MAP solutions, the AnnealedMAP algorithm is also able to solve many problems that are beyond the reach of previous approaches.