Nonlinear Causal Discovery via Kernel Anchor Regression

TL;DR

This paper introduces Kernel Anchor Regression (KAR), a novel method for nonlinear causal discovery that extends anchor regression to nonlinear settings using kernel methods, with proven convergence and superior performance.

Contribution

The paper develops a nonlinear extension of anchor regression called Kernel Anchor Regression, including theoretical guarantees and improved nonparametric variants.

Findings

KAR effectively learns nonlinear causal models.

Theoretical convergence and identifiability are established.

Experimental results outperform existing methods.

Abstract

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.