Gaussian Graphical Model Estimation with False Discovery Rate Control

TL;DR

This paper introduces a multiple testing approach for estimating high-dimensional Gaussian graphical models that effectively controls the false discovery rate, providing a rigorous alternative to regularization-based methods.

Contribution

It proposes a novel testing procedure with new test statistics for conditional dependence, enabling FDR control in GGM estimation.

Findings

Method controls false discovery rate asymptotically

Numerical experiments show good performance

Provides a rigorous alternative to regularization techniques

Abstract

This paper studies the estimation of high dimensional Gaussian graphical model (GGM). Typically, the existing methods depend on regularization techniques. As a result, it is necessary to choose the regularized parameter. However, the precise relationship between the regularized parameter and the number of false edges in GGM estimation is unclear. Hence, it is impossible to evaluate their performance rigorously. In this paper, we propose an alternative method by a multiple testing procedure. Based on our new test statistics for conditional dependence, we propose a simultaneous testing procedure for conditional dependence in GGM. Our method can control the false discovery rate (FDR) asymptotically. The numerical performance of the proposed method shows that our method works quite well.