A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment

• URL: http://arxiv.org/abs/2111.13226v4
• Date: Sun, 2 Jun 2024 17:48:34 GMT
• Title: A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment
• Authors: Robert Hu, Dino Sejdinovic, Robin J. Evans,
• Abstract summary: We develop a non-parametric method to test the textitdo-null hypothesis $H_0:; p(y|textit do(X=x))=p(y)$ against the general alternative. We demonstrate that backdoor-HSIC (bd-HSIC) is calibrated and has power for both binary and continuous treatments under a large number of confounders.
• Score: 18.791409397894835
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Causal inference grows increasingly complex as the number of confounders increases. Given treatments $X$, confounders $Z$ and outcomes $Y$, we develop a non-parametric method to test the \textit{do-null} hypothesis $H_0:\; p(y|\text{\it do}(X=x))=p(y)$ against the general alternative. Building on the Hilbert Schmidt Independence Criterion (HSIC) for marginal independence testing, we propose backdoor-HSIC (bd-HSIC) and demonstrate that it is calibrated and has power for both binary and continuous treatments under a large number of confounders. Additionally, we establish convergence properties of the estimators of covariance operators used in bd-HSIC. We investigate the advantages and disadvantages of bd-HSIC against parametric tests as well as the importance of using the do-null testing in contrast to marginal independence testing or conditional independence testing. A complete implementation can be found at \hyperlink{https://github.com/MrHuff/kgformula}{\texttt{https://github.com/MrHuff/kgformula}}.

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