A Stepwise Approach for High-Dimensional Gaussian Graphical Models

TL;DR

This paper introduces a novel stepwise algorithm for estimating high-dimensional Gaussian graphical models, leveraging the relationship between partial correlations and prediction errors, and demonstrates its superior performance over existing methods.

Contribution

The paper proposes a new stepwise algorithm that improves the detection of conditionally dependent variable pairs in high-dimensional Gaussian graphical models.

Findings

The proposed algorithm outperforms graphical lasso and CLIME in simulations.

It achieves better recovery of the true graph structure.

The method is effective in real-world applications.

Abstract

We present a stepwise approach to estimate high dimensional Gaussian graphical models. We exploit the relation between the partial correlation coefficients and the distribution of the prediction errors, and parametrize the model in terms of the Pearson correlation coefficients between the prediction errors of the nodes' best linear predictors. We propose a novel stepwise algorithm for detecting pairs of conditionally dependent variables. We show that the proposed algorithm outperforms existing methods such as the graphical lasso and CLIME in simulation studies and real life applications. In our comparison we report different performance measures that look at different desirable features of the recovered graph and consider several model settings.