Causal Network Inference via Group Sparse Regularization

TL;DR

This paper proposes a method using group sparse regularization to accurately infer sparse causal networks from limited data, introducing the false connection score as a key metric for successful recovery.

Contribution

It derives conditions for consistent network inference with Group Lasso, highlighting the false connection score's role and proposing a modified procedure to enhance accuracy.

Findings

Effective recovery with fewer observations than parameters

False connection score predicts recovery success

Modified gLasso improves causal direction accuracy

Abstract

This paper addresses the problem of inferring sparse causal networks modeled by multivariate auto-regressive (MAR) processes. Conditions are derived under which the Group Lasso (gLasso) procedure consistently estimates sparse network structure. The key condition involves a "false connection score." In particular, we show that consistent recovery is possible even when the number of observations of the network is far less than the number of parameters describing the network, provided that the false connection score is less than one. The false connection score is also demonstrated to be a useful metric of recovery in non-asymptotic regimes. The conditions suggest a modified gLasso procedure which tends to improve the false connection score and reduce the chances of reversing the direction of causal influence. Computational experiments and a real network based electrocorticogram (ECoG) simulation study demonstrate the effectiveness of the approach.