Learning mixed graphical models from data with p larger than n

TL;DR

This paper introduces a new statistical method for learning the structure of mixed graphical models with both discrete and continuous variables in high-dimensional settings where the number of variables exceeds the sample size.

Contribution

It proposes a novel approach based on limited-order correlations specifically designed for mixed data with p>>n, an area previously underexplored.

Findings

Method performs well on synthetic data.

Method demonstrates effectiveness on real data.

Provides a scalable solution for high-dimensional mixed graphical models.

Abstract

Structure learning of Gaussian graphical models is an extensively studied problem in the classical multivariate setting where the sample size n is larger than the number of random variables p, as well as in the more challenging setting when p>>n. However, analogous approaches for learning the structure of graphical models with mixed discrete and continuous variables when p>>n remain largely unexplored. Here we describe a statistical learning procedure for this problem based on limited-order correlations and assess its performance with synthetic and real data.