A general framework on conditions for constraint‐based causal learning
本文提出一个通用框架，通过属性概念表示约束型因果学习算法，研究其正确性条件，并给出PC算法的精确条件，为设计新算法提供范式。
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.