Learning binary undirected graph in low dimensional regime

TL;DR

This paper introduces a simple, closed-form estimator for the structure of undirected graphs in multivariate Bernoulli variables, effective in low-dimensional settings, with demonstrated practical applications and competitive performance.

Contribution

It presents a novel, closed-form estimator for graph structure in MBV distributions, specifically designed for low-dimensional regimes, with proven consistency and practical validation.

Findings

Estimator is consistent in low-dimensional regimes.

Performs well compared to state-of-the-art methods.

Successfully applied to real pediatric allergology data.

Abstract

Given a random sample extracted from a Multivariate Bernoulli Variable (MBV), we consider the problem of estimating the structure of the undirected graph for which the distribution is pairwise Markov and the parameters' vector of its exponential form. We propose a simple method that provides a closed form estimator of the parameters' vector and through its support also provides an estimate of the undirected graph associated to the MBV distribution. The estimator is proved to be consistent but it is feasible only in low-dimensional regimes. Synthetic examples illustrates its performance compared with another method that represents the state of the art in literature. Finally, the proposed procedure is used for the analysis of a real data set in the pediatric allergology area showing its practical efficiency.