Joint learning of multiple Granger causal networks via non-convex regularizations: Inference of group-level brain connectivity

TL;DR

This paper introduces a novel joint learning method for multiple Granger causal networks using non-convex regularizations, improving accuracy in low-sample scenarios and revealing brain connectivity differences in ADHD studies.

Contribution

It proposes a non-convex group norm regularization approach for joint estimation of multiple VAR models, enhancing network recovery and interpretability.

Findings

Improved network sparsity recovery over existing methods.

Identified causality differences in brain regions related to ADHD.

Validated approach on fMRI data aligning with clinical findings.

Abstract

This paper considers joint learning of multiple sparse Granger graphical models to discover underlying common and differential Granger causality (GC) structures across multiple time series. This can be applied to drawing group-level brain connectivity inferences from a homogeneous group of subjects or discovering network differences among groups of signals collected under heterogeneous conditions. By recognizing that the GC of a single multivariate time series can be characterized by common zeros of vector autoregressive (VAR) lag coefficients, a group sparse prior is included in joint regularized least-squares estimations of multiple VAR models. Group-norm regularizations based on group- and fused-lasso penalties encourage a decomposition of multiple networks into a common GC structure, with other remaining parts defined in individual-specific networks. Prior information about sparseness and sparsity patterns of desired GC networks are incorporated as relative weights, while a non-convex group norm in the penalty is proposed to enhance the accuracy of network estimation in low-sample settings. Extensive numerical results on simulations illustrated our method's improvements over existing sparse estimation approaches on GC network sparsity recovery. Our methods were also applied to available resting-state fMRI time series from the ADHD-200 data sets to learn the differences of causality mechanisms, called effective brain connectivity, between adolescents with ADHD and typically developing children. Our analysis revealed that parts of the causality differences between the two groups often resided in the orbitofrontal region and areas associated with the limbic system, which agreed with clinical findings and data-driven results in previous studies.