Nonlinear Causal Discovery via Kernel Anchor Regression
This work addresses causal discovery for researchers in fields requiring nonlinear causal modeling, though it appears incremental as it extends linear anchor regression to nonlinear cases.
The authors tackled the problem of learning causal relationships in nonlinear settings by proposing kernel anchor regression (KAR), which extends linear anchor regression to handle nonlinear structural equation models. Experimental results showed that KAR estimators outperformed existing baselines.
Learning causal relationships 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 the natural formulation using a classic two-stage least square estimator, we also study an improved variant that involves nonparametric 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.