# Total Stability of SVMs and Localized SVMs

arXiv: https://arxiv.org/abs/2101.12678 · HTML: https://mlsanity.com/paper/2101.12678/

## 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 (most cited first, 12 of 12)

- [Divide and Conquer Kernel Ridge Regression: A Distributed Algorithm with Minimax Optimal Rates](https://mlsanity.com/paper/1305.5029/) (2013)
- [Distributed learning with regularized least squares](https://mlsanity.com/paper/1608.03339/) (2016)
- [Distributed Kernel Ridge Regression with Communications](https://mlsanity.com/paper/2003.12210/) (2020)
- [Optimal Learning Rates for Localized SVMs](https://mlsanity.com/paper/1507.06615/) (2015)
- [Spatial Decompositions for Large Scale SVMs](https://mlsanity.com/paper/1612.00374/) (2016)
- [Total stability of kernel methods](https://mlsanity.com/paper/1709.07625/) (2017)
- [Learning rates for the risk of kernel based quantile regression estimators in additive models](https://mlsanity.com/paper/1405.3379/) (2014)
- [On the Robustness of Regularized Pairwise Learning Methods Based on Kernels](https://mlsanity.com/paper/1510.03267/) (2015)
- [Learning Rates for Kernel-Based Expectile Regression](https://mlsanity.com/paper/1702.07552/) (2017)
- [Universal Consistency and Robustness of Localized Support Vector Machines](https://mlsanity.com/paper/1703.06528/) (2017)
- [Quantitative Robustness of Localized Support Vector Machines](https://mlsanity.com/paper/1903.01334/) (2019)
- [On the robustness of kernel-based pairwise learning](https://mlsanity.com/paper/2010.15527/) (2020)

## Built on by (most cited first, 4 of 4)

- [Adaptive Parameter Selection for Kernel Ridge Regression](https://mlsanity.com/paper/2312.05885/) (2023)
- [On the Connection between Lp and Risk Consistency and its Implications on Regularized Kernel Methods](https://mlsanity.com/paper/2303.15210/) (2023)
- [Lp- and Risk Consistency of Localized SVMs](https://mlsanity.com/paper/2305.09385/) (2023)
- [Two-Stage Data Synthesization: A Statistics-Driven Restricted Trade-off between Privacy and Prediction](https://mlsanity.com/paper/2602.08657/) (2026)

## 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.