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Optimal and Structure-Adaptive CATE Estimation with Kernel Ridge Regression

arXiv 2602.18958 ↗First posted 21 Feb 2026stat.ME math.ST stat.MLcited by 0

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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.

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References · 23

  1. 2017Meta-learners for Estimating Heterogeneous Treatment Effects using Machine Learningcited by 478
  2. 2017Quasi-Oracle Estimation of Heterogeneous Treatment Effectscited by 332
  3. 2018Adaptivity of deep ReLU network for learning in Besov and mixed smooth Besov spaces: optimal rate and curse of dimensionalitycited by 162
  4. 2019Linearized two-layers neural networks in high dimensioncited by 155
  5. 2019Orthogonal Statistical Learningcited by 151
  6. 2021Nonparametric Estimation of Heterogeneous Treatment Effects: From Theory to Learning Algorithmscited by 144
  7. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 114
  8. 2022Optimally tackling covariate shift in RKHS-based nonparametric regressioncited by 54
  9. 2018Orthogonal Random Forest for Causal Inferencecited by 51
  10. 2020RealCause: Realistic Causal Inference Benchmarkingcited by 46
  11. 2020Kernel Methods for Causal Functions: Dose, Heterogeneous, and Incremental Response Curvescited by 36
  12. 2023On the Eigenvalue Decay Rates of a Class of Neural-Network Related Kernel Functions Defined on General Domainscited by 31
11 more
  1. 2023On the Optimality of Misspecified Kernel Ridge Regressioncited by 20
  2. 2023Pseudo-Labeling for Kernel Ridge Regression under Covariate Shiftcited by 17
  3. 2019Kernel Truncated Randomized Ridge Regression: Optimal Rates and Low Noise Accelerationcited by 12
  4. 2024Optimal Rates of Kernel Ridge Regression under Source Condition in Large Dimensionscited by 11
  5. 2020Minimax Optimal Nonparametric Estimation of Heterogeneous Treatment Effectscited by 9
  6. 2025Challenges in Statistics: A Dozen Challenges in Causality and Causal Inferencecited by 9
  7. 2023Kernel-based off-policy estimation without overlap: Instance optimality beyond semiparametric efficiencycited by 6
  8. 2024High-Dimensional Kernel Methods under Covariate Shift: Data-Dependent Implicit Regularizationcited by 4
  9. 2021Statistical inference using Regularized M-estimation in the reproducing kernel Hilbert space for handling missing datacited by 3
  10. 2023CATE Lasso: Conditional Average Treatment Effect Estimation with High-Dimensional Linear Regressioncited by 2
  11. 2025Transfer Learning of CATE with Kernel Ridge Regressioncited by 2

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