Conditions and Assumptions for Constraint-based Causal Structure Learning

TL;DR

This paper formalizes the conditions under which constraint-based causal structure learning algorithms can reliably identify causal graphs, even with unobserved variables, by relaxing faithfulness assumptions and providing testable criteria.

Contribution

It introduces conditions for natural constraint-based algorithms to output Markov equivalent causal graphs, extending the theoretical understanding of causal discovery with unobserved variables.

Findings

Conditions for algorithms to output Markov equivalent graphs

Relaxation of faithfulness assumption with testable criteria

Specialization of results for structural causal models

Abstract

We formalize constraint-based structure learning of the "true" causal graph from observed data when unobserved variables are also existent. We provide conditions for a "natural" family of constraint-based structure-learning algorithms that output graphs that are Markov equivalent to the causal graph. Under the faithfulness assumption, this natural family contains all exact structure-learning algorithms. We also provide a set of assumptions, under which any natural structure-learning algorithm outputs Markov equivalent graphs to the causal graph. These assumptions can be thought of as a relaxation of faithfulness, and most of them can be directly tested from (the underlying distribution) of the data, particularly when one focuses on structural causal models. We specialize the definitions and results for structural causal models.