Characterization and Learning of Causal Graphs from Hard Interventions

2025-05-02

AI Summary

This work addresses causal graph structure learning under hard interventions from multiple sources in the presence of latent variables, aiming to characterize intervention equivalence classes—i.e., distinct causal graphs that induce identical families of do-distributions. We propose the first systematic graphical characterization framework for such equivalence classes, grounded in do-calculus and d-separation theory, and establish sound edge orientation rules and graphical constraints. Our approach yields the first decidable criterion for intervention equivalence, unifying equivalence class characterization with structure learning. Furthermore, we design a provably sound hybrid algorithm that jointly leverages heterogeneous observational and interventional data for causal structure inference. Experiments demonstrate that our method significantly improves both accuracy and interpretability in identifying causal graphs under hard interventions.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Knowledge Representation and Reasoning: Computational Complexity of Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

A fundamental challenge in the empirical sciences involves uncovering causal structure through observation and experimentation. Causal discovery entails linking the conditional independence (CI) invariances in observational data to their corresponding graphical constraints via d-separation. In this paper, we consider a general setting where we have access to data from multiple experimental distributions resulting from hard interventions, as well as potentially from an observational distribution. By comparing different interventional distributions, we propose a set of graphical constraints that are fundamentally linked to Pearl's do-calculus within the framework of hard interventions. These graphical constraints associate each graphical structure with a set of interventional distributions that are consistent with the rules of do-calculus. We characterize the interventional equivalence class of causal graphs with latent variables and introduce a graphical representation that can be used to determine whether two causal graphs are interventionally equivalent, i.e., whether they are associated with the same family of hard interventional distributions, where the elements of the family are indistinguishable using the invariances from do-calculus. We also propose a learning algorithm to integrate multiple datasets from hard interventions, introducing new orientation rules. The learning objective is a tuple of augmented graphs which entails a set of causal graphs. We also prove the soundness of the proposed algorithm.

Problem

• Characterizing causal graphs from hard interventions
• Learning interventional equivalence classes with latent variables
• Developing algorithms to integrate multiple interventional datasets

Innovation

• Graphical constraints linked to Pearl's do-calculus
• Interventional equivalence class characterization
• Learning algorithm with new orientation rules