# Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression

arXiv: https://arxiv.org/abs/2602.18958 · HTML: https://mlsanity.com/paper/2602.18958/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 31 references that are in the map.
- First posted on arXiv 21 Feb 2026.

## Builds on (most cited first, 23 of 23)

- [Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learning](https://mlsanity.com/paper/1706.03461/) (2017)
- [Quasi-Oracle Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/1712.04912/) (2017)
- [Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionality](https://mlsanity.com/paper/1810.08033/) (2018)
- [Linearized two-layers neural networks in high dimension](https://mlsanity.com/paper/1904.12191/) (2019)
- [Orthogonal Statistical Learning](https://mlsanity.com/paper/1901.09036/) (2019)
- [Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithms](https://mlsanity.com/paper/2101.10943/) (2021)
- [Sobolev Norm Learning Rates for Regularized Least-Squares Algorithm](https://mlsanity.com/paper/1702.07254/) (2017)
- [Optimally tackling covariate shift in RKHS-based nonparametric regression](https://mlsanity.com/paper/2205.02986/) (2022)
- [Orthogonal Random Forest for Causal Inference](https://mlsanity.com/paper/1806.03467/) (2018)
- [RealCause: Realistic Causal Inference Benchmarking](https://mlsanity.com/paper/2011.15007/) (2020)
- [Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curves](https://mlsanity.com/paper/2010.04855/) (2020)
- [On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domains](https://mlsanity.com/paper/2305.02657/) (2023)
- [On the Optimality of Misspecified Kernel Ridge Regression](https://mlsanity.com/paper/2305.07241/) (2023)
- [Pseudo-Labeling for Kernel Ridge Regression under Covariate Shift](https://mlsanity.com/paper/2302.10160/) (2023)
- [Kernel Truncated Randomized Ridge Regression: Optimal Rates and Low Noise Acceleration](https://mlsanity.com/paper/1905.10680/) (2019)
- [Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensions](https://mlsanity.com/paper/2401.01270/) (2024)
- [Minimax Optimal Nonparametric Estimation of Heterogeneous Treatment Effects](https://mlsanity.com/paper/2002.06471/) (2020)
- [Challenges in Statistics: A Dozen Challenges in Causality and Causal Inference](https://mlsanity.com/paper/2508.17099/) (2025)
- [Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiency](https://mlsanity.com/paper/2301.06240/) (2023)
- [High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularization](https://mlsanity.com/paper/2406.03171/) (2024)
- [Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing data](https://mlsanity.com/paper/2107.07371/) (2021)
- [CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regression](https://mlsanity.com/paper/2310.16819/) (2023)
- [Transfer Learning of CATE with Kernel Ridge Regression](https://mlsanity.com/paper/2502.11331/) (2025)

## Abstract (arXiv)

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.