Interaction Information for Causal Inference: The Case of Directed Triangle

TL;DR

This paper explores how interaction information, which can be negative unlike mutual information, can be used to determine causal directions in a three-variable triangle topology.

Contribution

It introduces a method leveraging the negative property of interaction information to infer causal directions in a specific variable topology.

Findings

Interaction information can be negative, indicating causal influence direction.

The method applies to triangle topologies under mild assumptions.

It provides a new approach for causal inference in multivariate systems.

Abstract

Interaction information is one of the multivariate generalizations of mutual information, which expresses the amount information shared among a set of variables, beyond the information, which is shared in any proper subset of those variables. Unlike (conditional) mutual information, which is always non-negative, interaction information can be negative. We utilize this property to find the direction of causal influences among variables in a triangle topology under some mild assumptions.