Learning Nonlinear Causal Effect via Kernel Anchor Regression

Wenqi Shi, Wenkai Xu
Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, PMLR 216:1942-1952, 2023.

Abstract

Learning causal effects is a fundamental problem in science. Anchor regression has been developed to address this problem for a large class of causal graphical models, though the relationships between the variables are assumed to be linear. In this work, we tackle the nonlinear setting by proposing kernel anchor regression (KAR). Beyond a classic two-stage least square (2SLS) estimator, we also study an improved variant that involves nonparametric kernel regression in three separate stages. We provide convergence results for the proposed KAR estimators and the identifiability conditions for KAR to learn the nonlinear structural equation models (SEM). Experimental results demonstrate the superior performances of the proposed KAR estimators over existing baselines.

Cite this Paper

BibTeX
@InProceedings{pmlr-v216-shi23a, title = {Learning Nonlinear Causal Effect via Kernel Anchor Regression}, author = {Shi, Wenqi and Xu, Wenkai}, booktitle = {Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence}, pages = {1942--1952}, year = {2023}, editor = {Evans, Robin J. and Shpitser, Ilya}, volume = {216}, series = {Proceedings of Machine Learning Research}, month = {31 Jul--04 Aug}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v216/shi23a/shi23a.pdf}, url = {https://proceedings.mlr.press/v216/shi23a.html}, abstract = {Learning causal effects is a fundamental problem in science. Anchor regression has been developed to address this problem for a large class of causal graphical models, though the relationships between the variables are assumed to be linear. In this work, we tackle the nonlinear setting by proposing kernel anchor regression (KAR). Beyond a classic two-stage least square (2SLS) estimator, we also study an improved variant that involves nonparametric kernel regression in three separate stages. We provide convergence results for the proposed KAR estimators and the identifiability conditions for KAR to learn the nonlinear structural equation models (SEM). Experimental results demonstrate the superior performances of the proposed KAR estimators over existing baselines.} }
Endnote
%0 Conference Paper %T Learning Nonlinear Causal Effect via Kernel Anchor Regression %A Wenqi Shi %A Wenkai Xu %B Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2023 %E Robin J. Evans %E Ilya Shpitser %F pmlr-v216-shi23a %I PMLR %P 1942--1952 %U https://proceedings.mlr.press/v216/shi23a.html %V 216 %X Learning causal effects is a fundamental problem in science. Anchor regression has been developed to address this problem for a large class of causal graphical models, though the relationships between the variables are assumed to be linear. In this work, we tackle the nonlinear setting by proposing kernel anchor regression (KAR). Beyond a classic two-stage least square (2SLS) estimator, we also study an improved variant that involves nonparametric kernel regression in three separate stages. We provide convergence results for the proposed KAR estimators and the identifiability conditions for KAR to learn the nonlinear structural equation models (SEM). Experimental results demonstrate the superior performances of the proposed KAR estimators over existing baselines.
APA
Shi, W. & Xu, W.. (2023). Learning Nonlinear Causal Effect via Kernel Anchor Regression. Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research 216:1942-1952 Available from https://proceedings.mlr.press/v216/shi23a.html.

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