Bounding Probabilities of Causation with Partial Causal Diagrams

2026-02-16

AI Summary

This work proposes a general framework for bounding probabilistic causation at the individual level, where exact identification is typically infeasible—especially in realistic settings involving incomplete causal graphs or non-binary variables. By systematically incorporating partial causal knowledge, such as structural or statistical constraints, into a constrained optimization problem, the method leverages counterfactual reasoning and constraint programming to compute tight bounds on probabilistic causal effects. Unlike traditional approaches that rely on fully specified causal graphs, strong identifiability assumptions, or binary variables, this framework operates under weaker conditions while preserving theoretical rigor, thereby substantially broadening its applicability to practical decision-making scenarios.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

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: Attacks and countermeasures in recommendation systems

Abstract

Probabilities of causation are fundamental to individual-level explanation and decision making, yet they are inherently counterfactual and not point-identifiable from data in general. Existing bounds either disregard available covariates, require complete causal graphs, or rely on restrictive binary settings, limiting their practical use. In real-world applications, causal information is often partial but nontrivial. This paper proposes a general framework for bounding probabilities of causation using partial causal information. We show how the available structural or statistical information can be systematically incorporated as constraints in a optimization programming formulation, yielding tighter and formally valid bounds without full identifiability. This approach extends the applicability of probabilities of causation to realistic settings where causal knowledge is incomplete but informative.

Problem

• probabilities of causation
• partial causal diagrams
• counterfactual inference
• causal bounds
• incomplete causal knowledge

Innovation

• probabilities of causation
• partial causal diagrams
• counterfactual reasoning
• optimization-based bounding
• causal inference