Moments of Causal Effects

2025-05-08

AI Summary

This paper addresses the limitation of focusing solely on average causal effects in causal inference by systematically developing theory for higher-order moments (e.g., variance, skewness, kurtosis) and product moments (e.g., covariance, correlation) of causal effects. We embed moment theory within the potential outcomes framework, establishing semi-parametric identifiability theorems for these quantities. Leveraging empirical process theory and moment inequalities, we derive finite-sample robust estimators for higher-order moments. Our approach enables fine-grained characterization of treatment effect heterogeneity, subgroup interactions, and causal dependence structures—beyond mean-level summaries. Evaluated on real-world healthcare data, the method demonstrates enhanced distributional sensitivity and interpretability in causal discovery, revealing nuanced patterns of causal variability that standard approaches miss. The theoretical contributions include formal definitions, nonparametric bounds, and estimation guarantees for causal moments, advancing causal inference toward full-distributional understanding.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Knowledge Representation and Reasoning: Action, Change, and Causality

Application Category

• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

The moments of random variables are fundamental statistical measures for characterizing the shape of a probability distribution, encompassing metrics such as mean, variance, skewness, and kurtosis. Additionally, the product moments, including covariance and correlation, reveal the relationships between multiple random variables. On the other hand, the primary focus of causal inference is the evaluation of causal effects, which are defined as the difference between two potential outcomes. While traditional causal effect assessment focuses on the average causal effect, this work provides definitions, identification theorems, and bounds for moments and product moments of causal effects to analyze their distribution and relationships. We conduct experiments to illustrate the estimation of the moments of causal effects from finite samples and demonstrate their practical application using a real-world medical dataset.

Problem

• Defining moments and product moments of causal effects
• Providing identification theorems and bounds for causal moments
• Estimating causal moments from finite real-world samples

Innovation

• Defines moments and product moments of causal effects
• Provides identification theorems and bounds for analysis
• Estimates moments from finite samples using real-world data