conditional ggm estimation

This study addresses the challenge of modeling how external risk factors influence multivariate conditional independence structures within a unified graphical framework. To this end, the authors propose a novel class of models termed “profile graphical models,” formally defining this family for the first time and showing that both multigraphs and chain graphs arise as special cases. They further establish the compatibility of profile graphical models with the independence interpretation of two-block LWF chain graphs. Building upon a continuous spike-and-slab prior, they develop a Bayesian inference procedure for Gaussian undirected profile graphical models and devise an efficient EM algorithm for implementation. Empirical evaluations on both synthetic data and protein signaling networks in acute myeloid leukemia demonstrate that the proposed model yields more parsimonious network representations and significantly improves the capture of patient heterogeneity compared to existing approaches.

This paper addresses the problem of modeling discrete dynamic graphs under high-dimensional covariate-dependent dependencies. We propose a class of covariate-driven dynamic discrete graph models that capture smoothly evolving network structures among discrete random variables as functions of covariates, subsuming the dynamic Ising model as a special case. Methodologically, we introduce a pseudo-likelihood-based high-dimensional parameter estimation framework to circumvent the intractability of exact likelihood computation, and integrate a birth-death MCMC algorithm for adaptive sparse graph structure selection. Theoretically and empirically, our approach achieves both statistical consistency and computational efficiency in high-dimensional settings, substantially improving identification accuracy and inferential robustness for covariate-dependent dynamic networks. This work provides a novel paradigm for modeling conditional dependence structures in complex systems—such as neural activity and social contagion—where interactions evolve with contextual covariates.

This study addresses the problem of accurately estimating the proportion of non-zero partial correlation edges in high-dimensional Gaussian graphical models to quantify the complexity of conditional dependence structures. By reframing graph complexity estimation as a large-scale multiple hypothesis testing problem, the approach leverages edge-specific p-values combined with Storey’s method to estimate the proportion of true null hypotheses, enabling robust inference of the precision matrix’s sparsity structure under false discovery rate control. Theoretically, the work establishes convergence of the empirical p-value distribution under high-dimensional weak dependence settings—common in genetic association studies—and reveals the asymptotic upward bias of the Schweder–Spjøtvoll estimator, leading to a more accurate complexity estimator. Simulations demonstrate that the proposed method effectively and robustly recovers graph complexity across diverse high-dimensional scenarios.

This paper addresses the challenge of modeling variable dependencies in mixed-type data—encompassing continuous, discrete, categorical, and zero-inflated count variables. We propose the first Bayesian pairwise graphical model that is both theoretically rigorous and practically robust. Methodologically, we innovatively integrate spike-and-slab priors into mixed graphical models and perform joint structure learning via conditional-likelihood-based MCMC sampling. The framework rigorously preserves both global and local Markov properties and natively accommodates missing-at-random (MAR) missingness. Experiments demonstrate substantial improvements over state-of-the-art methods across four simulated missing-data scenarios. Applied to real-world adolescent eating disorder data, our model successfully uncovers dynamic shifts in cognitive–behavioral association structures before and after treatment, revealing interpretable neurocognitive pathways underlying therapeutic change.

Existing approaches to modeling spatial processes struggle to effectively capture conditional independence among multiple variables, hindering the construction of interpretable partial correlation networks. This work introduces a novel class of stationary multivariate Gaussian processes—termed “spectrally inverted”—which, for the first time, rigorously defines and decomposes partial correlation coefficients at the process level, establishing a direct link to Gaussian graphical models. The proposed framework subsumes several classical models, extends naturally to nonstationary settings, and, through precision matrix modulation and factorization of partial cross-correlation functions, exposes fundamental limitations of existing methods in representing graph structures. Both theoretical analysis and empirical experiments demonstrate that the approach accurately recovers spatial conditional dependence structures and reveals inherent structural deficiencies in models such as linear coregionalization.

This study addresses the challenge of estimating conditional independence graphs from high-dimensional Gaussian data while simultaneously controlling false discoveries and accurately identifying edges. The authors propose a novel Bayesian framework that integrates adaptive priors capturing node degree heterogeneity, edge sparsity, and graph topological structure, coupled with a multiple testing procedure to achieve false discovery rate (FDR) control in graph inference. Computationally, the method leverages an adaptive elastic net penalty and a variational expectation-maximization algorithm for efficient optimization. In simulations, the approach demonstrates substantially improved statistical power while rigorously maintaining FDR control. Applications to breast cancer gene expression and financial return networks yield sparse, stable, and biologically or economically interpretable conditional dependence graphs, particularly excelling in heterogeneous networks containing hub nodes.

Existing methods for modeling protein–protein interaction networks often neglect prior biological knowledge and assume a static network structure across individuals, thereby failing to capture covariate-driven, personalized interaction patterns. This work proposes a conditional Gaussian graphical model that, for the first time, integrates database-derived priors and covariate-dependent relationships within a unified framework. By employing structured weighted L1 regularization, the method simultaneously incorporates population-level priors while preserving context-specific perturbations. It effectively distinguishes between universal interactions and disease-specific alterations. Applied to proteomic data from the UK Biobank (n = 49,129), the approach identified 34 network centrality–based biomarkers and six functionally coherent protein modules, with several biomarkers detectable only through connectivity changes rather than differential expression.

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.