Causal attribution with confidence

2025-04-11

AI Summary

This paper addresses the “cause-of-effect” attribution problem, focusing on statistical inference for the Probability of Necessity (PoN). Under non-monotonic settings, PoN is not point-identified, and its sharp bounds are non-smooth functionals—rendering conventional asymptotic theory and estimation methods inapplicable. To resolve this, we introduce a mild boundary differentiability condition that ensures pathwise differentiability of the PoN bounds. Leveraging semiparametric efficiency theory and influence function methodology, we construct the first asymptotically efficient estimators for these bounds. Building upon them, we derive tighter, less conservative confidence intervals that fully exploit covariate information. Our approach is theoretically justified under both randomized experiments and observational studies. It substantially improves the precision and practical applicability of PoN inference, offering valid, robust, and efficient statistical tools for causal attribution analysis.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Nonmonotonic Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems

Abstract

To answer questions of"causes of effects", the probability of necessity is introduced for assessing whether or not an observed outcome was caused by an earlier treatment. However, the statistical inference for probability of necessity is understudied due to several difficulties, which hinders its application in practice. The evaluation of the probability of necessity involves the joint distribution of potential outcomes, and thus it is in general not point identified and one can at best obtain lower and upper bounds even in randomized experiments, unless certain monotonicity assumptions on potential outcomes are made. Moreover, these bounds are non-smooth functionals of the observed data distribution and standard estimation and inference methods cannot be directly applied. In this paper, we investigate the statistical inference for the probability of necessity in general situations where it may not be point identified. We introduce a mild margin condition to tackle the non-smoothness, under which the bounds become pathwise differentiable. We establish the semiparametric efficiency theory and propose novel asymptotically efficient estimators of the bounds, and further construct confidence intervals for the probability of necessity based on the proposed bounds estimators. The resultant confidence intervals are less conservative than existing methods and can effectively make use of the observed covariates.

Problem

• Statistical inference for probability of necessity is understudied
• Evaluating probability of necessity involves non-smooth functionals
• Existing methods for confidence intervals are too conservative

Innovation

• Introduces margin condition for non-smoothness
• Develops semiparametric efficiency theory
• Proposes efficient estimators and confidence intervals