High-Dimensional Graphical Latent Gaussian Copula Model with Covariates

Music City Center 

In this work, we propose a high-dimensional Graphical Latent Gaussian Copula Model that extends traditional Gaussian graphical models by incorporating external covariates. The model assumes a latent Gaussian structure where observed variables arise through monotonic transformations, allowing for a flexible representation of conditional dependencies. We introduce a novel approach in which the mean and precision matrix of the latent variables are modeled as functions of covariates, capturing population-level and individual-specific network structures.

To estimate the model parameters, we develop an efficient estimation procedure that leverages bridge functions to infer latent correlations from observed data. The estimation is further refined using a sparse group lasso penalty to encourage structured sparsity.

Simulation studies and real-world applications demonstrate the model's ability to recover latent dependency structures and identify covariate-driven variations in network connectivity. This framework has broad applicability in biomedical and social sciences, where latent interactions play a crucial role in data analysis.

Copula Model

High Dimensional Data

Graphical Model

Precision Matrix Estimation

Sparse Group Lasso

Covariate-Dependent Networks 

Section on Statistics in Imaging