Submodular Decomposition Framework for Inference in Associative Markov Networks with Global Constraints

TL;DR

This paper introduces a novel submodular decomposition framework for efficient inference in associative Markov networks with global constraints, addressing NP-hardness in finding most probable states.

Contribution

The paper proposes a new submodular decomposition method that preserves graph structure and efficiently incorporates global constraints in MRF inference.

Findings

The approach effectively handles global constraints in MRFs.

Theoretical analysis supports the method's properties.

Demonstrated applicability on various problems.

Abstract

In the paper we address the problem of finding the most probable state of discrete Markov random field (MRF) with associative pairwise terms. Although of practical importance, this problem is known to be NP-hard in general. We propose a new type of MRF decomposition, submodular decomposition (SMD). Unlike existing decomposition approaches SMD decomposes the initial problem into subproblems corresponding to a specific class label while preserving the graph structure of each subproblem. Such decomposition enables us to take into account several types of global constraints in an efficient manner. We study theoretical properties of the proposed approach and demonstrate its applicability on a number of problems.