A General Framework on Conditions for Constraint-based Causal Learning

TL;DR

This paper introduces a general framework for understanding correctness conditions in constraint-based causal learning algorithms, enabling better design and analysis of such algorithms.

Contribution

It formalizes the notion of properties to unify correctness conditions, derives exact conditions for the PC algorithm, and discusses implications for causal discovery.

Findings

Exact correctness conditions for the PC algorithm.

Sparsest Markov representation is the weakest correctness condition.

Pearl-minimality needs strengthening for causal learning beyond faithfulness.

Abstract

Most constraint-based causal learning algorithms provably return the correct causal graph under certain correctness conditions, such as faithfulness. By representing any constraint-based causal learning algorithm using the notion of a property, we provide a general framework to obtain and study correctness conditions for these algorithms. From the framework, we provide exact correctness conditions for the PC algorithm, which are then related to the correctness conditions of some other existing causal discovery algorithms. The framework also suggests a paradigm for designing causal learning algorithms which allows for the correctness conditions of algorithms to be controlled for before designing the actual algorithm, and has the following implications. We show that the sparsest Markov representation condition is the weakest correctness condition for algorithms that output ancestral graphs or directed acyclic graphs satisfying any existing notions of minimality. We also reason that Pearl-minimality is necessary for meaningful causal learning but not sufficient to relax the faithfulness condition and, as such, has to be strengthened, such as by including background knowledge, for causal learning beyond faithfulness.