Identification of Conditional Interventional Distributions

TL;DR

This paper develops graphical criteria and algorithms for identifying conditional interventional distributions in causal models, and proves the completeness of do-calculus for this identification problem.

Contribution

It introduces necessary and sufficient conditions for computing these distributions and demonstrates the completeness of do-calculus in this context.

Findings

Provided a graphical condition for unique computation of conditional interventional distributions.

Developed an algorithm to compute these distributions when the condition holds.

Proved the completeness of do-calculus for the identification problem.

Abstract

The subject of this paper is the elucidation of effects of actions from causal assumptions represented as a directed graph, and statistical knowledge given as a probability distribution. In particular, we are interested in predicting conditional distributions resulting from performing an action on a set of variables and, subsequently, taking measurements of another set. We provide a necessary and sufficient graphical condition for the cases where such distributions can be uniquely computed from the available information, as well as an algorithm which performs this computation whenever the condition holds. Furthermore, we use our results to prove completeness of do-calculus [Pearl, 1995] for the same identification problem.