Direct Estimation of Differential Functional Graphical Models

TL;DR

This paper introduces a method for directly estimating the difference between two high-dimensional functional graphical models, enabling efficient detection of changes in complex data like EEG signals.

Contribution

It proposes a novel approach that directly estimates graph differences in high-dimensional functional data, avoiding separate graph estimations and demonstrating consistency.

Findings

Method is consistent in high-dimensional settings.

Effective in uncovering brain connectivity differences in EEG data.

Performs well in simulation studies.

Abstract

We consider the problem of estimating the difference between two functional undirected graphical models with shared structures. In many applications, data are naturally regarded as high-dimensional random function vectors rather than multivariate scalars. For example, electroencephalography (EEG) data are more appropriately treated as functions of time. In these problems, not only can the number of functions measured per sample be large, but each function is itself an infinite dimensional object, making estimation of model parameters challenging. We develop a method that directly estimates the difference of graphs, avoiding separate estimation of each graph, and show it is consistent in certain high-dimensional settings. We illustrate finite sample properties of our method through simulation studies. Finally, we apply our method to EEG data to uncover differences in functional brain connectivity between alcoholics and control subjects.