A General Framework for Constraint-based Causal Learning

2024-08-14

arXiv.org

AI Summary

This work addresses the formal modeling of correctness conditions for constraint-based causal learning algorithms. Method: We propose a unifying framework that decouples correctness conditions into two orthogonal components: (i) the relationship between the observational distribution and the true causal DAG, and (ii) constraints solely expressible in terms of the observed distribution—thereby unifying the theoretical foundations of classical algorithms such as PC. Contribution/Results: We derive the first exact correctness condition for the PC algorithm; prove that the sparse Markov representation condition is the weakest sufficient minimality condition among existing notions, and show that Pearl’s minimality alone cannot relax the faithfulness assumption. By integrating placeholder-based modeling, minimality analysis of maximal ancestral graphs and DAGs, and synergistic constraint testing with graph-theoretic inference, we establish a unified correctness verification framework. This clarifies the theoretical boundaries among faithfulness, minimality, and domain knowledge, significantly enhancing the interpretability and applicability of constraint-based causal discovery.

Technology Category

Reasoning under Uncertainty: CausalityMachine Learning: Causal LearningConstraint Satisfaction and Optimization: Constraint Learning and Acquisition

Application Category

Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphsSemantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semanticsWeb Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

By representing any constraint-based causal learning algorithm via a placeholder property, we decompose the correctness condition into a part relating the distribution and the true causal graph, and a part that depends solely on the distribution. This provides a general framework to obtain correctness conditions for causal learning, and has the following implications. We provide exact correctness conditions for the PC algorithm, which are then related to correctness conditions of some other existing causal discovery algorithms. We show that the sparsest Markov representation condition is the weakest correctness condition resulting from existing notions of minimality for maximal ancestral graphs and directed acyclic graphs. We also reason that additional knowledge than just Pearl-minimality is necessary for causal learning beyond faithfulness.

Problem

• General framework for correctness conditions in causal learning algorithms
• Exact correctness conditions for PC algorithm and related methods
• Weakest correctness condition for sparsest Markov representation output

Innovation

• General framework for constraint-based causal learning
• Exact correctness conditions for PC algorithm
• Sparsest Markov representation as weakest condition