Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression

TL;DR

This paper introduces an optimal, adaptive kernel ridge regression method for estimating conditional average treatment effects (CATEs) that leverages structural simplicity in the contrast function to improve estimation accuracy and adaptivity.

Contribution

It develops a unified two-stage KRR approach that achieves minimax rates based on the contrast function's complexity and includes a model-selection step for unknown regularity.

Findings

Attains minimax rates governed by contrast function complexity.

Provides a model-selection procedure with oracle inequality.

Demonstrates improved CATE estimation in RKHS settings.

Abstract

We propose an optimal algorithm for estimating conditional average treatment effects (CATEs) when response functions lie in a reproducing kernel Hilbert space (RKHS). We study settings in which the contrast function is structurally simpler than the nuisance functions: (i) it lies in a lower-complexity RKHS with faster eigenvalue decay, (ii) it satisfies a source condition relative to the nuisance kernel, or (iii) it depends on a known low-dimensional covariate representation. We develop a unified two-stage kernel ridge regression (KRR) method that attains minimax rates governed by the complexity of the contrast function rather than the nuisance class, in terms of both sample size and overlap. We also show that a simple model-selection step over candidate contrast spaces and regularization levels yields an oracle inequality, enabling adaptation to unknown CATE regularity.