Quantifying causal influences

TL;DR

This paper introduces a new measure of causal influence based on information theory, satisfying natural postulates and addressing limitations of existing measures, with validation on simulated time-series data.

Contribution

It proposes a novel causal strength measure using relative entropy, fulfilling specific postulates, and demonstrates its advantages over existing measures through experiments.

Findings

The new measure satisfies all proposed postulates.

Existing measures often fail to meet the postulates.

Experimental results support the effectiveness of the new measure.

Abstract

Many methods for causal inference generate directed acyclic graphs (DAGs) that formalize causal relations between $n$ variables. Given the joint distribution on all these variables, the DAG contains all information about how intervening on one variable changes the distribution of the other $n-1$ variables. However, quantifying the causal influence of one variable on another one remains a nontrivial question. Here we propose a set of natural, intuitive postulates that a measure of causal strength should satisfy. We then introduce a communication scenario, where edges in a DAG play the role of channels that can be locally corrupted by interventions. Causal strength is then the relative entropy distance between the old and the new distribution. Many other measures of causal strength have been proposed, including average causal effect, transfer entropy, directed information, and information flow. We explain how they fail to satisfy the postulates on simple DAGs of $\leq3$ nodes. Finally, we investigate the behavior of our measure on time-series, supporting our claims with experiments on simulated data.