51: High-dimensional Functional Graphical Modeling in the Presence of Hidden Confounders

Music City Center 

Functional graphical models have recently been employed to capture the conditional independence structure of high-dimensional functional data and functional time series. However, real-world datasets often encounter challenges due to latent processes that can confound multiple variables. To address this issue, we propose a novel estimator for functional graphical models that accounts for the presence of unobserved confounders. Our estimator is constructed using the projection of the right singular functions of the multivariate random functions, and is the functional extension of the Right Singular Vector Projection estimation for random variable. Unlike previous approaches that focus on "spiked" confounders and rely on removing principal components from multivariate functional PCA, our method is designed to accommodate a broader range of confounder effects, from strong and spiked to weak. We establish the consistency of our estimator in the high-dimensional setting, and demonstrate its effectiveness through synthetic simulations and fMRI data analysis

Functional Data Analysis

Graphical Models

High-dimensional Statistics

Structure Learning

Hidden Confounders

Covariance Estimator 

Section on Statistical Learning and Data Science