Learning Nonlinear Causal Effect via Kernel Anchor Regression

Wenqi Shi, Wenkai Xu

Keywords: Causal Learning, Kernel method

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.