Network Granger Causality with Inherent Grouping Structure

TL;DR

This paper introduces a thresholded Group Lasso method for estimating high-dimensional network structures with inherent grouping, demonstrating its consistency and superior performance through simulations.

Contribution

It proposes a novel thresholded Group Lasso estimator tailored for Granger causality in networks with group structures, with proven asymptotic consistency.

Findings

The method accurately recovers network structures in simulations.

It outperforms existing techniques in various scenarios.

The estimator is asymptotically consistent.

Abstract

The problem of estimating high-dimensional network models arises naturally in the analysis of many physical, biological and socio-economic systems. Examples include stock price fluctuations in financial markets and gene regulatory networks representing effects of regulators (transcription factors) on regulated genes in genetics. We aim to learn the structure of the network over time employing the framework of Granger causal models under the assumptions of sparsity of its edges and inherent grouping structure among its nodes. We introduce a thresholded variant of the Group Lasso estimator for discovering Granger causal interactions among the nodes of the network. Asymptotic results on the consistency of the new estimation procedure are developed. The performance of the proposed methodology is assessed through an extensive set of simulation studies and comparisons with existing techniques.