Estimation and Inference for Causal Explainability

Weihan Zhang, Zijun Gao
Proceedings of the Fifth Conference on Causal Learning and Reasoning, PMLR 323:1380-1423, 2026.

Abstract

Understanding how much each variable contributes to an outcome is a central question across disciplines. A causal view of explainability is favorable for its ability in uncovering underlying mechanisms and generalizing to new contexts. Based on a family of causal explainability quantities, we develop methods for their estimation and inference. In particular, we construct a one-step correction estimator using semi-parametric efficiency theory, which explicitly leverages the joint structure of variables and outcome to reduce the asymptotic variance. For a null hypothesis on the boundary, i.e., zero explainability, we show its equivalence to Fisher’s sharp null, which motivates a randomization-based inference procedure. Finally, we illustrate the empirical efficacy of our approach through simulations as well as an immigration experiment dataset, where we investigate how individual features and their interactions shape public opinion toward admitting immigrants.

Cite this Paper

BibTeX
@InProceedings{pmlr-v323-zhang26a, title = {Estimation and Inference for Causal Explainability}, author = {Zhang, Weihan and Gao, Zijun}, booktitle = {Proceedings of the Fifth Conference on Causal Learning and Reasoning}, pages = {1380--1423}, year = {2026}, editor = {Mazaheri, Bijan and Hanson, Niels Richard}, volume = {323}, series = {Proceedings of Machine Learning Research}, month = {06--08 Apr}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v323/main/assets/zhang26a/zhang26a.pdf}, url = {https://proceedings.mlr.press/v323/zhang26a.html}, abstract = {Understanding how much each variable contributes to an outcome is a central question across disciplines. A causal view of explainability is favorable for its ability in uncovering underlying mechanisms and generalizing to new contexts. Based on a family of causal explainability quantities, we develop methods for their estimation and inference. In particular, we construct a one-step correction estimator using semi-parametric efficiency theory, which explicitly leverages the joint structure of variables and outcome to reduce the asymptotic variance. For a null hypothesis on the boundary, i.e., zero explainability, we show its equivalence to Fisher’s sharp null, which motivates a randomization-based inference procedure. Finally, we illustrate the empirical efficacy of our approach through simulations as well as an immigration experiment dataset, where we investigate how individual features and their interactions shape public opinion toward admitting immigrants.} }
Endnote
%0 Conference Paper %T Estimation and Inference for Causal Explainability %A Weihan Zhang %A Zijun Gao %B Proceedings of the Fifth Conference on Causal Learning and Reasoning %C Proceedings of Machine Learning Research %D 2026 %E Bijan Mazaheri %E Niels Richard Hanson %F pmlr-v323-zhang26a %I PMLR %P 1380--1423 %U https://proceedings.mlr.press/v323/zhang26a.html %V 323 %X Understanding how much each variable contributes to an outcome is a central question across disciplines. A causal view of explainability is favorable for its ability in uncovering underlying mechanisms and generalizing to new contexts. Based on a family of causal explainability quantities, we develop methods for their estimation and inference. In particular, we construct a one-step correction estimator using semi-parametric efficiency theory, which explicitly leverages the joint structure of variables and outcome to reduce the asymptotic variance. For a null hypothesis on the boundary, i.e., zero explainability, we show its equivalence to Fisher’s sharp null, which motivates a randomization-based inference procedure. Finally, we illustrate the empirical efficacy of our approach through simulations as well as an immigration experiment dataset, where we investigate how individual features and their interactions shape public opinion toward admitting immigrants.
APA
Zhang, W. & Gao, Z.. (2026). Estimation and Inference for Causal Explainability. Proceedings of the Fifth Conference on Causal Learning and Reasoning, in Proceedings of Machine Learning Research 323:1380-1423 Available from https://proceedings.mlr.press/v323/zhang26a.html.

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