Granger causality and the inverse Ising problem

TL;DR

This paper explores how autoregressive methods, including Granger causality, can be used to infer connections in Ising models, even with asymmetric and multi-spin interactions, and compares linear and nonlinear causality measures.

Contribution

It demonstrates the applicability of autoregressive and Granger causality techniques to learn Ising model connections, including asymmetric and multi-spin interactions, with theoretical and practical insights.

Findings

Linear Granger causality is twice the transfer entropy in the weak coupling limit.

L1 regularization effectively detects sparse spin interactions with limited data.

Nonlinear Granger causality relates to multispin interactions.

Abstract

We study Ising models for describing data and show that autoregressive methods may be used to learn their connections, also in the case of asymmetric connections and for multi-spin interactions. For each link the linear Granger causality is two times the corresponding transfer entropy (i.e. the information flow on that link) in the weak coupling limit. For sparse connections and a low number of samples, the L1 regularized least squares method is used to detect the interacting pairs of spins. Nonlinear Granger causality is related to multispin interactions.