Gaussian Graphical Models for Functional Connectivity Analysis: A Statistical Review with Applications to Alzheimer's Disease

2026-04-11

AI Summary

This study addresses the lack of systematic evaluation of various sparse precision matrix estimation methods in Gaussian graphical models (GGMs) for brain functional connectivity analysis and their implications in neuroimaging applications. For the first time, it comprehensively assesses mainstream regularization approaches—including graphical lasso (glasso), adaptive glasso, SCAD, MCP, CLIME, and TIGER—under realistic neuroimaging conditions using both data-driven simulations and an Alzheimer’s disease cohort. The findings reveal substantial differences among GGM methods in estimating functional connectivity and conducting downstream network analyses, thereby offering empirical guidance for method selection in disease-related research. To enhance reproducibility and accessibility, the authors also introduce spice, an open-source R package implementing these methods.

Technology Category

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

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Security and Privacy: Large-scale security measurements

Abstract

Functional connectivity analysis is an important tool for characterizing interactions among brain regions, particularly in studies of neurodegenerative disorders such as Alzheimer's disease (AD). Gaussian graphical models (GGMs) provide a promising statistical framework for estimating functional connectivity by capturing conditional dependence relationships among brain regions. Although a variety of regularized precision matrix estimators have been proposed to estimate sparse conditional dependency structures for GGMs, their comparative performance and practical implications for neuroimaging studies are not well understood. In this work, we present a comprehensive statistical review and empirical evaluation of widely used GGM estimation methods, including the graphical lasso (glasso), ridge-based glasso, graphical elastic net, adaptive glasso, smoothly clipped absolute deviation (SCAD), minimax concave penalty (MCP), constrained $\ell_1$ minimization for inverse matrix estimation (CLIME), and tuning-insensitive graph estimation and regression (TIGER). Their performance is evaluated through extensive data-driven simulations designed to reflect realistic neuroimaging settings, along with an application to an AD cohort study to illustrate methodological differences and their impact on downstream network analysis. In addition, a user-friendly R package, spice, is provided to facilitate implementation and enhance the reproducibility of empirical studies.

Problem

• Gaussian graphical models
• functional connectivity
• Alzheimer's disease
• precision matrix estimation
• neuroimaging

Innovation

• Gaussian graphical models
• functional connectivity
• regularized precision matrix estimation
• neuroimaging
• Alzheimer's disease