A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment
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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 do-null hypothesis H_0: p(y| 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 https://github.com/MrHuff/kgformula.
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