Statistical inference using debiased group graphical lasso for multiple sparse precision matrices

2025-10-06

AI Summary

This paper addresses statistical inference for multiple Gaussian graphical models sharing a common sparse precision matrix structure. We propose a debiased group graphical Lasso method that circumvents conventional incoherence-type conditions, yielding asymptotically unbiased estimators. Under moderate high-dimensionality ($p_n = o(n^{1/2})$), the method enables simultaneous hypothesis testing for nonzero entries across all group-specific precision matrices. Theoretically, the estimator achieves an $O_P(sqrt{log p / n})$ convergence rate in estimation error, enjoys model selection consistency, and exhibits asymptotic normality. Simulation studies demonstrate substantial improvements in statistical power and confidence interval coverage compared to existing approaches. Applied to real fMRI data, the method successfully identifies stable, cross-population brain functional connectivity patterns—thereby validating its statistical reliability and practical utility.

Technology Category

• Reasoning under Uncertainty: Graphical Models
• Machine Learning: Graph-based Machine Learning
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Debiasing group graphical lasso estimates enables statistical inference when multiple Gaussian graphical models share a common sparsity pattern. We analyze the estimation properties of group graphical lasso, establishing convergence rates and model selection consistency under irrepresentability conditions. Based on these results, we construct debiased estimators that are asymptotically Gaussian, allowing hypothesis testing for linear combinations of precision matrix entries across populations. We also investigate regimes where irrepresentibility conditions does not hold, showing that consistency can still be attained in moderately high-dimensional settings. Simulation studies confirm the theoretical results, and applications to real datasets demonstrate the practical utility of the method.

Problem

• Debiasing group graphical lasso for statistical inference
• Enabling hypothesis testing across multiple Gaussian graphical models
• Establishing consistency in high-dimensional sparse precision matrices

Innovation

• Debiased group graphical lasso enables statistical inference
• Asymptotically Gaussian estimators allow hypothesis testing
• Method maintains consistency in high-dimensional settings