Bounding Probabilities of Causation with Partial Causal Diagrams

TL;DR

This paper introduces a flexible framework for bounding probabilities of causation using partial causal diagrams, enabling more accurate causal inference in real-world scenarios with incomplete causal information.

Contribution

It develops an optimization-based method to incorporate partial causal knowledge, providing tighter bounds without requiring full causal graph identifiability.

Findings

Framework yields tighter bounds than existing methods.

Applicable to real-world scenarios with partial causal information.

Formal validation of bounds under incomplete causal knowledge.

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.