Learning non-parametric Markov networks with mutual information

TL;DR

This paper introduces a non-parametric approach to learn Markov network structures for continuous data using mutual information estimators, effectively capturing non-linear dependencies without distributional assumptions.

Contribution

It presents a novel non-parametric independence test combined with an efficient algorithm for structure learning, outperforming existing methods on synthetic datasets with non-linear dependencies.

Findings

More accurate structure learning on synthetic data with non-linear dependencies

Effective non-parametric independence testing for continuous variables

Improved performance over competing methods

Abstract

We propose a method for learning Markov network structures for continuous data without invoking any assumptions about the distribution of the variables. The method makes use of previous work on a non-parametric estimator for mutual information which is used to create a non-parametric test for multivariate conditional independence. This independence test is then combined with an efficient constraint-based algorithm for learning the graph structure. The performance of the method is evaluated on several synthetic data sets and it is shown to learn considerably more accurate structures than competing methods when the dependencies between the variables involve non-linearities.