A Kernel Test for Causal Association via Noise Contrastive Backdoor Adjustment

TL;DR

This paper introduces a non-parametric kernel-based test, bd-HSIC, for assessing causal effects in complex scenarios with many confounders, improving causal inference accuracy.

Contribution

It develops the backdoor-HSIC method for non-parametric causal testing, extending HSIC to handle confounders and treatments, with proven calibration and power.

Findings

bd-HSIC is calibrated and powerful for binary and continuous treatments.

The method is robust with a large number of confounders.

Convergence properties of the estimators are established.

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}}.