mlsanityData to 14 Oct 2026

Total Stability of SVMs and Localized SVMs

arXiv 2101.12678 ↗First posted 29 Jan 2021stat.ML cs.LGcited by 4

Not on the map. Why?

Abstract (arXiv)

Regularized kernel-based methods such as support vector machines (SVMs) typically depend on the underlying probability measure P (respectively an empirical measure Dn in applications) as well as on the regularization parameter λ and the kernel k. Whereas classical statistical robustness only considers the effect of small perturbations in P, the present paper investigates the influence of simultaneous slight variations in the whole triple (P,λ,k), respectively (Dn,λn,k), on the resulting predictor. Existing results from the literature are considerably generalized and improved. In order to also make them applicable to big data, where regular SVMs suffer from their super-linear computational requirements, we show how our results can be transferred to the context of localized learning. Here, the effect of slight variations in the applied regionalization, which might for example stem from changes in P respectively Dn, is considered as well.

Key facts. Cited by 4 papers in the map (data through 14 Oct 2026). Builds on 12 of its 69 references that are in the map. First posted on arXiv 29 Jan 2021.

Builds on

12 of 69 references.

References · 12

  1. 2013Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Ratescited by 65
  2. 2016Distributed learning with regularized least squarescited by 42
  3. 2020Distributed Kernel Ridge Regression with Communicationscited by 14
  4. 2015Optimal Learning Rates for Localized SVMscited by 13
  5. 2016Spatial Decompositions for Large Scale SVMscited by 5
  6. 2017Total stability of kernel methodscited by 5
  7. 2014Learning rates for the risk of kernel based quantile regression estimators in additive modelscited by 4
  8. 2015On the Robustness of Regularized Pairwise Learning Methods Based on Kernelscited by 4
  9. 2017Learning Rates for Kernel-Based Expectile Regressioncited by 4
  10. 2017Universal Consistency and Robustness of Localized Support Vector Machinescited by 4
  11. 2019Quantitative Robustness of Localized Support Vector Machinescited by 2
  12. 2020On the robustness of kernel-based pairwise learningcited by 1

Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2023: 3; 2024: 0; 2025: 0; 2026: 1.

4 papers.

  1. 2023Adaptive Parameter Selection for Kernel Ridge Regressioncited by 3
  2. 2023On the Connection between Lp and Risk Consistency and its Implications on Regularized Kernel Methodscited by 1
  3. 2023Lp- and Risk Consistency of Localized SVMscited by 0
  4. 2026Two-Stage Data Synthesization: A Statistics-Driven Restricted Trade-off between Privacy and Predictioncited by 0