An Algorithm for Deciding if a Set of Observed Independencies Has a Causal Explanation

TL;DR

This paper introduces an algorithm to determine whether a set of observed independencies can be perfectly explained by a single causal model represented as a directed acyclic graph, addressing the fundamental problem of causal explanation consistency.

Contribution

It presents a novel algorithm that decides the existence of a causal DAG consistent with all observed independence statements, advancing causal inference methods.

Findings

Algorithm effectively tests for the existence of a consistent causal DAG.

The algorithm can produce a causal model if one exists.

Provides a systematic method for causal explanation validation.

Abstract

In a previous paper [Pearl and Verma, 1991] we presented an algorithm for extracting causal influences from independence information, where a causal influence was defined as the existence of a directed arc in all minimal causal models consistent with the data. In this paper we address the question of deciding whether there exists a causal model that explains ALL the observed dependencies and independencies. Formally, given a list M of conditional independence statements, it is required to decide whether there exists a directed acyclic graph (dag) D that is perfectly consistent with M, namely, every statement in M, and no other, is reflected via dseparation in D. We present and analyze an effective algorithm that tests for the existence of such a day, and produces one, if it exists.