Interaction Information for Causal Inference: The Case of Directed Triangle
This work addresses causal inference for researchers in statistics and machine learning, but it appears incremental as it applies an existing information-theoretic concept to a specific topology.
The paper tackled the problem of inferring causal direction in triangle-structured variable relationships by leveraging the property that interaction information can be negative, enabling direction identification under mild assumptions.
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.