Moments of Causal Effects

Yuta Kawakami, Jin Tian
Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, PMLR 286:2011-2043, 2025.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v286-kawakami25a, title = {Moments of Causal Effects}, author = {Kawakami, Yuta and Tian, Jin}, booktitle = {Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence}, pages = {2011--2043}, year = {2025}, editor = {Chiappa, Silvia and Magliacane, Sara}, volume = {286}, series = {Proceedings of Machine Learning Research}, month = {21--25 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v286/main/assets/kawakami25a/kawakami25a.pdf}, url = {https://proceedings.mlr.press/v286/kawakami25a.html}, 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.} }
Endnote
%0 Conference Paper %T Moments of Causal Effects %A Yuta Kawakami %A Jin Tian %B Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2025 %E Silvia Chiappa %E Sara Magliacane %F pmlr-v286-kawakami25a %I PMLR %P 2011--2043 %U https://proceedings.mlr.press/v286/kawakami25a.html %V 286 %X 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.
APA
Kawakami, Y. & Tian, J.. (2025). Moments of Causal Effects. Proceedings of the Forty-first Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 286:2011-2043 Available from https://proceedings.mlr.press/v286/kawakami25a.html.

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