Discovering the Markov network structure

TL;DR

This paper introduces a new algorithm for discovering the structure of Markov networks based on the supermodularity of information content and demonstrates its application on a specific discrete distribution.

Contribution

It provides a novel proof of supermodularity, leverages decomposability for structure discovery, and illustrates the algorithm on a distribution with zero-probability realizations.

Findings

Algorithm successfully discovers Markov network structure.

Supermodularity of information content is proven and utilized.

Application on a specific distribution confirms effectiveness.

Abstract

In this paper a new proof is given for the supermodularity of information content. Using the decomposability of the information content an algorithm is given for discovering the Markov network graph structure endowed by the pairwise Markov property of a given probability distribution. A discrete probability distribution is given for which the equivalence of Hammersley-Clifford theorem is fulfilled although some of the possible vector realizations are taken on with zero probability. Our algorithm for discovering the pairwise Markov network is illustrated on this example, too.