mlsanityData to 7 Oct 2026

Distributed learning with regularized least squares

arXiv 1608.03339 ↗First posted 11 Aug 2016cs.LG stat.MLcited by 42

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Abstract (arXiv)

We study distributed learning with the least squares regularization scheme in a reproducing kernel Hilbert space (RKHS). By a divide-and-conquer approach, the algorithm partitions a data set into disjoint data subsets, applies the least squares regularization scheme to each data subset to produce an output function, and then takes an average of the individual output functions as a final global estimator or predictor. We show with error bounds in expectation in both the L2-metric and RKHS-metric that the global output function of this distributed learning is a good approximation to the algorithm processing the whole data in one single machine. Our error bounds are sharp and stated in a general setting without any eigenfunction assumption. The analysis is achieved by a novel second order decomposition of operator differences in our integral operator approach. Even for the classical least squares regularization scheme in the RKHS associated with a general kernel, we give the best learning rate in the literature.

Key facts. Cited by 42 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Aug 2016.

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Citing papers per year: 2021: 9; 2022: 5; 2023: 13; 2024: 4; 2025: 4; 2026: 7.

42 papers.

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  1. 2023On the Optimality of Misspecified Spectral Algorithmscited by 28
  2. 2022Distribution Regression with Sliced Wasserstein Kernelscited by 18
  3. 2022Capacity dependent analysis for functional online learning algorithmscited by 10
  4. 2021Federated Gaussian Process: Convergence, Automatic Personalization and Multi-fidelity Modelingcited by 8
  5. 2022Statistical Optimality of Divide and Conquer Kernel-based Functional Linear Regressioncited by 8
  6. 2021Hyperdimensional Computing for Efficient Distributed Classification with Randomized Neural Networkscited by 7
  7. 2021Data splitting improves statistical performance in overparametrized regimescited by 6
  8. 2021Radial Basis Function Approximation with Distributively Stored Data on Spherescited by 6
  9. 2023Random Smoothing Regularization in Kernel Gradient Descent Learningcited by 6
  10. 2021ParK: Sound and Efficient Kernel Ridge Regression by Feature Space Partitionscited by 5
  11. 2023Minibatch and Local SGD: Algorithmic Stability and Linear Speedup in Generalizationcited by 5
  12. 2021Total Stability of SVMs and Localized SVMscited by 4
30 more
  1. 2024Optimal Kernel Quantile Learning with Random Featurescited by 4
  2. 2021Nystr"om Regularization for Time Series Forecastingcited by 3
  3. 2023Adaptive Parameter Selection for Kernel Ridge Regressioncited by 3
  4. 2022Coefficient-based Regularized Distribution Regressioncited by 2
  5. 2023Distributed Gradient Descent for Functional Learningcited by 2
  6. 2023Adaptive Distributed Kernel Ridge Regression: A Feasible Distributed Learning Scheme for Data Siloscited by 2
  7. 2023Distributed Uncertainty Quantification of Kernel Interpolation on Spherescited by 2
  8. 2025Fixed-Gaussian Spectral Algorithms: Minimax Optimal Rates for Misspecified Learning and Transfercited by 2
  9. 2023Sketching with Spherical Designs for Noisy Data Fitting on Spherescited by 1
  10. 2023Distributed Semi-Supervised Sparse Statistical Inferencecited by 1
  11. 2023On regularized polynomial functional regressioncited by 1
  12. 2024Distributed Learning with Discretely Observed Functional Datacited by 1
  13. 2025Striking the Perfect Balance: Preserving Privacy While Boosting Utility in Collaborative Medical Prediction Platformscited by 1
  14. 2026Beyond Cross-Validation: Adaptive Parameter Selection for Kernel-Based Gradient Descentscited by 1
  15. 2021Uncertainty quantification for distributed regressioncited by 0
  16. 2021Oversampling Divide-and-conquer for Response-skewed Kernel Ridge Regressioncited by 0
  17. 2022Local SGD in Overparameterized Linear Regressioncited by 0
  18. 2023Kernel-Based Distributed Q-Learning: A Scalable Reinforcement Learning Approach for Dynamic Treatment Regimescited by 0
  19. 2023Lp- and Risk Consistency of Localized SVMscited by 0
  20. 2023Convergence analysis of online algorithms for vector-valued kernel regressioncited by 0
  21. 2024Integral Operator Approaches for Scattered Data Fitting on Spherescited by 0
  22. 2024Multiparameter regularization and aggregation in the context of polynomial functional regressioncited by 0
  23. 2025Sobolev norm inconsistency of kernel interpolationcited by 0
  24. 2025Theory of Decentralized Robust Kernel-Based Learningcited by 0
  25. 2026Two-Stage Data Synthesization: A Statistics-Driven Restricted Trade-off between Privacy and Predictioncited by 0
  26. 2026On the Stability and Generalization of First-order Bilevel Minimax Optimizationcited by 0
  27. 2026Sketched Linear Contrastive Learning: Approximation, Optimization, and Statistical Scalingcited by 0
  28. 2026Scalable Operator Learning via Nystr"om Approximation With Denoising Applicationscited by 0
  29. 2026Adaptive Regularization for Random Features: A Neighboring Early-Stopping Rule with Oracle-Rate Guaranteescited by 0
  30. 2026FedeRage: Provably Convergent Agnostic Federated Learning under General Client Driftcited by 0