mlsanityData to 7 Oct 2026

Sobolev Norm Learning Rates for Conditional Mean Embeddings

arXiv 2105.07446 ↗First posted 16 May 2021stat.ML cs.LG math.STcited by 7

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Abstract (arXiv)

We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the misspecifed setting, where the target operator is not Hilbert-Schmidt or bounded with respect to the input/output RKHSs. We demonstrate that in certain parameter regimes, we can achieve uniform convergence rates in the output RKHS. We hope our analyses will allow the much broader application of conditional mean embeddings to more complex ML/RL settings involving infinite dimensional RKHSs and continuous state spaces.

Key facts. Cited by 7 papers in the map (data through 7 Oct 2026). Builds on 9 of its 25 references that are in the map. First posted on arXiv 16 May 2021.

Builds on

9 of 25 references.

References · 9

  1. 2015An Introduction to Matrix Concentration Inequalitiescited by 391
  2. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
  3. 2020A Measure-Theoretic Approach to Kernel Conditional Mean Embeddingscited by 86
  4. 2018Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spacescited by 59
  5. 2017Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spacescited by 48
  6. 2019A Rigorous Theory of Conditional Mean Embeddingscited by 31
  7. 2018Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral Algorithmscited by 22
  8. 2020Nonparametric approximation of conditional expectation operatorscited by 21
  9. 2020Kernel Autocovariance Operators of Stationary Processes: Estimation and Convergencecited by 3

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Cited by year

Citing papers per year: 2022: 4; 2023: 1; 2024: 2.

7 papers.

  1. 2022Optimal Rates for Regularized Conditional Mean Embedding Learningcited by 50
  2. 2022Minimax Optimal Kernel Operator Learning via Multilevel Trainingcited by 13
  3. 2022Spectral Representation Learning for Conditional Moment Modelscited by 12
  4. 2024Nonparametric Instrumental Variable Regression through Stochastic Approximate Gradientscited by 6
  5. 2022Optimal Learning Rates for Regularized Least-Squares with a Fourier Capacity Conditioncited by 2
  6. 2024Spectrally Transformed Kernel Regressioncited by 2
  7. 2023Supervised learning with probabilistic morphisms and kernel mean embeddingscited by 1