Two Gaussian regularization methods for time-varying networks

TL;DR

This paper introduces two regularization methods for estimating time-varying Gaussian graphical models, emphasizing computational efficiency and tuning parameter selection, with applications to brain connectivity analysis.

Contribution

It proposes two novel algorithms based on elastic net and fused LASSO for modeling dynamic precision matrices in time-varying networks.

Findings

Effective algorithms for sparse, time-varying precision matrices.

Application to fMRI data reveals differences in brain connectivity.

Guidelines for tuning parameter selection.

Abstract

We model time-varying network data as realizations from multivariate Gaussian distributions with precision matrices that change over time. To facilitate parameter estimation, we require not only that each precision matrix at any given time point be sparse, but also that precision matrices at neighboring time points be similar. We accomplish this with two different algorithms, by generalizing the elastic net and the fused LASSO, respectively. Our main focuses are efficient computational algorithms and convenient degree-of-freedom formulae for choosing tuning parameters. We illustrate our methods with two simulation studies. By applying them to an fMRI data set, we also detect some interesting differences in brain connectivity between healthy individuals and ADHD patients.