Joint Functional Gaussian Graphical Models

TL;DR

This paper introduces a joint estimation method for multiple functional graphical models that accounts for shared and unique dependence structures across subgroups, improving accuracy in complex data like EEG.

Contribution

It proposes a hierarchical penalty-based approach for joint graph estimation that captures both common and subgroup-specific structures, with a developed computation method for non-convex optimization.

Findings

Outperforms existing methods in simulated scenarios

Effectively captures shared and subgroup-specific dependencies

Successfully applied to EEG data to distinguish brain networks

Abstract

Functional graphical models explore dependence relationships of random processes. This is achieved through estimating the precision matrix of the coefficients from the Karhunen-Loeve expansion. This paper deals with the problem of estimating functional graphs that consist of the same random processes and share some of the dependence structure. By estimating a single graph we would be shrouding the uniqueness of different sub groups within the data. By estimating a different graph for each sub group we would be dividing our sample size. Instead, we propose a method that allows joint estimation of the graphs while taking into account the intrinsic differences of each sub group. This is achieved by a hierarchical penalty that first penalizes on a common level and then on an individual level. We develop a computation method for our estimator that deals with the non-convex nature of the objective function. We compare the performance of our method with existing ones on a number of different simulated scenarios. We apply our method to an EEG data set that consists of an alcoholic and a non-alcoholic group, to construct brain networks.