# Gaussian Graphical Model Estimation with False Discovery Rate Control

arXiv: https://arxiv.org/abs/1306.0976 · HTML: https://mlsanity.com/paper/1306.0976/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Jun 2013.

## Built on by (most cited first, 9 of 9)

- [Interpretable Machine Learning for Discovery: Statistical Challenges & Opportunities](https://mlsanity.com/paper/2308.01475/) (2023)
- [False Discovery Rate Control for Gaussian Graphical Models via Neighborhood Screening](https://mlsanity.com/paper/2401.09979/) (2024)
- [Directional FDR Control for Sub-Gaussian Sparse GLMs](https://mlsanity.com/paper/2105.00393/) (2021)
- [Inference for Similarity and Alignability between Noisy High-Dimensional Datasets](https://mlsanity.com/paper/2511.21074/) (2025)
- [Two-stage Hypothesis Tests for Variable Interactions with FDR Control](https://mlsanity.com/paper/2209.00077/) (2022)
- [Alteration Detection of Tensor Dependence Structure via Sparsity-Exploited Reranking Algorithm](https://mlsanity.com/paper/2310.08798/) (2023)
- [DART2: a robust multiple testing method to smartly leverage helpful or misleading ancillary information](https://mlsanity.com/paper/2409.03618/) (2024)
- [Inference for High-Dimensional Sparse Spectral Precision Matrices](https://mlsanity.com/paper/2606.07986/) (2026)
- [High-dimensional Gaussian Graphical Model Testing for Long-Memory Time Series](https://mlsanity.com/paper/2609.30565/) (2026)

## Abstract (arXiv)

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.