mlsanityData to 7 Oct 2026

Online nonparametric regression with Sobolev kernels

arXiv 2102.03594 ↗First posted 6 Feb 2021math.ST cs.LG stat.MLcited by 5

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Abstract (arXiv)

In this work we investigate the variation of the online kernelized ridge regression algorithm in the setting of d-dimensional adversarial nonparametric regression. We derive the regret upper bounds on the classes of Sobolev spaces Wpβ(X), p≥ 2, β>fracdp. The upper bounds are supported by the minimax regret analysis, which reveals that in the cases β> fracd2 or p=∞ these rates are (essentially) optimal. Finally, we compare the performance of the kernelized ridge regression forecaster to the known non-parametric forecasters in terms of the regret rates and their computational complexity as well as to the excess risk rates in the setting of statistical (i.i.d.) nonparametric regression.

Key facts. Cited by 5 papers in the map (data through 7 Oct 2026). Builds on 11 of its 48 references that are in the map. First posted on arXiv 6 Feb 2021.

Builds on

11 of 48 references.

References · 11

  1. 2017Sobolev Norm Learning Rates for Regularized Least-Squares Algorithmcited by 113
  2. 2015Less is More: Nystr"om Computational Regularizationcited by 89
  3. 2018Statistical Optimality of Stochastic Gradient Descent on Hard Learning Problems through Multiple Passescited by 69
  4. 2016Optimal Rates For Regularization Of Statistical Inverse Learning Problemscited by 68
  5. 2013Relative Loss Bounds for On-line Density Estimation with the Exponential Family of Distributionscited by 59
  6. 2018Optimal Rates for Spectral Algorithms with Least-Squares Regression over Hilbert Spacescited by 59
  7. 2015A Chaining Algorithm for Online Nonparametric Regressioncited by 16
  8. 2018Uniform regret bounds over Rd for the sequential linear regression problem with the square losscited by 14
  9. 2019Efficient online learning with kernels for adversarial large scale problemscited by 12
  10. 2018Online Improper Learning with an Approximation Oraclecited by 11
  11. 2020Interpolation and Learning with Scale Dependent Kernelscited by 7

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2022: 2; 2023: 0; 2024: 1; 2025: 1; 2026: 1.

5 papers.

  1. 2022Scale-free Unconstrained Online Learning for Curved Lossescited by 13
  2. 2022Learning Lipschitz Functions by GD-trained Shallow Overparameterized ReLU Neural Networkscited by 5
  3. 2024Structured Prediction in Online Learningcited by 2
  4. 2025Minimax Adaptive Online Nonparametric Regression over Besov Spacescited by 1
  5. 2026Dynamic Regret for Online Regression in RKHS via Discounted VAW and Subspace Approximationcited by 0