Towards Complete Causal Explanation with Expert Knowledge

TL;DR

This paper develops methods to restrict Markov equivalence classes of maximal ancestral graphs using expert knowledge, providing new orientation rules, algorithms, and theoretical insights, especially in the presence of latent confounding.

Contribution

It introduces new graphical orientation rules, algorithms for incorporating expert knowledge, and extends existing theory to latent confounding scenarios.

Findings

Proved properties for the entire Markov equivalence class.

Developed sound orientation rules for adding expert knowledge.

Provided algorithms for constructing and verifying restricted essential ancestral graphs.

Abstract

We study the problem of restricting a Markov equivalence class of maximal ancestral graphs (MAGs) to only those MAGs that contain certain edge marks, which we refer to as expert or orientation knowledge. Such a restriction of the Markov equivalence class can be uniquely represented by a restricted essential ancestral graph. Our contributions are several-fold. First, we prove certain properties for the entire Markov equivalence class including a conjecture from Ali et al. (2009). Second, we present several new sound graphical orientation rules for adding orientation knowledge to an essential ancestral graph. We also show that some orientation rules of Zhang (2008b) are not needed for restricting the Markov equivalence class with orientation knowledge. Third, we provide an algorithm for including this orientation knowledge and show that in certain settings the output of our algorithm is a restricted essential ancestral graph. Finally, outside of the specified settings, we provide an algorithm for checking whether a graph is a restricted essential graph and discuss its runtime. This work can be seen as a generalization of Meek (1995) to settings which allow for latent confounding.