Directed information and Pearl's causal calculus

TL;DR

This paper explores the connections between Pearl's causal calculus and information theory, introducing an information-theoretic approach to causal inference and extending the back-door criterion for causal effect identification.

Contribution

It establishes a link between Pearl's intervention-based causal formalism and information-theoretic measures, proposing an information-theoretic version of the back-door criterion.

Findings

Conditional directed information can identify causal effects from passive observations.

The back-door criterion is analogous to statistical sufficiency in causal inference.

Connections between causal calculus and information theory are formalized.

Abstract

Probabilistic graphical models are a fundamental tool in statistics, machine learning, signal processing, and control. When such a model is defined on a directed acyclic graph (DAG), one can assign a partial ordering to the events occurring in the corresponding stochastic system. Based on the work of Judea Pearl and others, these DAG-based "causal factorizations" of joint probability measures have been used for characterization and inference of functional dependencies (causal links). This mostly expository paper focuses on several connections between Pearl's formalism (and in particular his notion of "intervention") and information-theoretic notions of causality and feedback (such as causal conditioning, directed stochastic kernels, and directed information). As an application, we show how conditional directed information can be used to develop an information-theoretic version of Pearl's "back-door" criterion for identifiability of causal effects from passive observations. This suggests that the back-door criterion can be thought of as a causal analog of statistical sufficiency.