General Probabilities of Causation with Causal Knowledge

2026-08-12

AI Summary

This study addresses the challenge of identifying multivalued causal probabilities—such as the probability of necessity (PN), sufficiency (PS), and necessity and sufficiency (PNS)—when direct observational data are unavailable. Existing bounds for these quantities are often too loose to accurately characterize individual-level causal effects, particularly in non-binary settings. To overcome this limitation, this work proposes a novel approach that integrates causal knowledge from covariates and mediators into the structural causal model and counterfactual reasoning framework, yielding substantially tighter bounds for multivalued variables. Theoretical analysis and simulation experiments demonstrate that the proposed method significantly outperforms current non-binary bounds, markedly improving the precision of multivalued causal effect estimation and overcoming key limitations of traditional approaches in non-binary contexts.

Abstract

Probabilities of causation (PoCs) characterize individual causal responses that cannot be directly observed and therefore generally require partial identification. Tian and Pearl first derived theoretically sharp bounds for binary PoCs, including the probability of necessity (PN), the probability of sufficiency (PS), and the probability of necessity and sufficiency (PNS). Mueller et al. subsequently tightened the bounds for binary PNS by incorporating causal information encoded in covariates and mediators. More recently, Li and Pearl, as well as Shu et al., extended PoCs to multivalued settings and derived corresponding theoretical bounds. These developments naturally raise the question of whether additional causal knowledge can further tighten the bounds in multivalued settings. This paper addresses this question by deriving tighter bounds for multivalued PoCs through the incorporation of causal information encoded in covariates and mediators. We illustrate the theoretical results with toy examples, while simulation studies further demonstrate that the proposed bounds are tighter than existing nonbinary bounds.

Problem

• Probabilities of Causation
• multivalued settings
• causal knowledge
• partial identification
• bounds tightening

Innovation

• Probabilities of Causation
• Multivalued Causal Inference
• Partial Identification
• Covariates and Mediators
• Sharp Bounds