Distributed Anytime MAP Inference

TL;DR

This paper introduces a distributed anytime algorithm for MAP inference in graphical models, leveraging linear programming relaxation and Dantzig-Wolfe decomposition to efficiently handle large-scale problems with improved solution quality.

Contribution

It presents a novel distributed algorithm that solves MAP inference via linear programming and decomposition, enabling scalability and better solutions than existing methods.

Findings

Outperforms current algorithms in solution quality

Scales effectively to large problems

Guarantees convergence to the optimal solution

Abstract

We present a distributed anytime algorithm for performing MAP inference in graphical models. The problem is formulated as a linear programming relaxation over the edges of a graph. The resulting program has a constraint structure that allows application of the Dantzig-Wolfe decomposition principle. Subprograms are defined over individual edges and can be computed in a distributed manner. This accommodates solutions to graphs whose state space does not fit in memory. The decomposition master program is guaranteed to compute the optimal solution in a finite number of iterations, while the solution converges monotonically with each iteration. Formulating the MAP inference problem as a linear program allows additional (global) constraints to be defined; something not possible with message passing algorithms. Experimental results show that our algorithm's solution quality outperforms most current algorithms and it scales well to large problems.