Characterization and Learning of Causal Graphs with Latent Confounders and Post-treatment Selection from Interventional Data

2025-09-30

AI Summary

Causal graph identification remains challenging under concurrent latent confounding and post-intervention selection bias. Method: We propose a novel causal discovery framework that defines the FI-Markov equivalence class and introduces the F-PAG (Falsification-aware Partial Ancestral Graph) to explicitly model post-intervention selection mechanisms, thereby distinguishing selection-induced spurious dependencies from genuine causal responses. By jointly leveraging observational and multi-source interventional data, we design the F-FCI algorithm, which exploits distributional shift patterns to perform structure learning over a refined equivalence class. Contribution/Results: Experiments on synthetic and real-world datasets demonstrate that our method simultaneously recovers the underlying causal structure, latent confounders, and post-intervention selection mechanisms. It significantly improves causal graph recovery accuracy and overcomes the fundamental limitations of conventional PAG-based approaches in modeling selection bias.

Technology Category

• Machine Learning: Causal Learning
• Reasoning under Uncertainty: Causality
• Constraint 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 graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Interventional causal discovery seeks to identify causal relations by leveraging distributional changes introduced by interventions, even in the presence of latent confounders. Beyond the spurious dependencies induced by latent confounders, we highlight a common yet often overlooked challenge in the problem due to post-treatment selection, in which samples are selectively included in datasets after interventions. This fundamental challenge widely exists in biological studies; for example, in gene expression analysis, both observational and interventional samples are retained only if they meet quality control criteria (e.g., highly active cells). Neglecting post-treatment selection may introduce spurious dependencies and distributional changes under interventions, which can mimic causal responses, thereby distorting causal discovery results and challenging existing causal formulations. To address this, we introduce a novel causal formulation that explicitly models post-treatment selection and reveals how its differential reactions to interventions can distinguish causal relations from selection patterns, allowing us to go beyond traditional equivalence classes toward the underlying true causal structure. We then characterize its Markov properties and propose a Fine-grained Interventional equivalence class, named FI-Markov equivalence, represented by a new graphical diagram, F-PAG. Finally, we develop a provably sound and complete algorithm, F-FCI, to identify causal relations, latent confounders, and post-treatment selection up to $mathcal{FI}$-Markov equivalence, using both observational and interventional data. Experimental results on synthetic and real-world datasets demonstrate that our method recovers causal relations despite the presence of both selection and latent confounders.

Problem

• Addressing post-treatment selection bias in causal discovery from interventional data
• Modeling latent confounders and selection effects simultaneously in causal graphs
• Developing equivalence classes and algorithms for accurate causal relation identification

Innovation

• Novel causal formulation models post-treatment selection explicitly
• Introduces FI-Markov equivalence class with F-PAG representation
• Develops F-FCI algorithm for causal discovery with interventions