# Lp- and Risk Consistency of Localized SVMs

arXiv: https://arxiv.org/abs/2305.09385 · HTML: https://mlsanity.com/paper/2305.09385/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 72 references that are in the map.
- First posted on arXiv 16 May 2023.

## Builds on (most cited first, 18 of 18)

- [Self-Normalizing Neural Networks](https://mlsanity.com/paper/1706.02515/) (2017)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [Generalization error of random features and kernel methods: hypercontractivity and kernel matrix concentration](https://mlsanity.com/paper/2101.10588/) (2021)
- [Random Features for Kernel Approximation: A Survey on Algorithms, Theory, and Beyond](https://mlsanity.com/paper/2004.11154/) (2020)
- [Less is More: Nystr"om Computational Regularization](https://mlsanity.com/paper/1507.04717/) (2015)
- [Kernel methods through the roof: handling billions of points efficiently](https://mlsanity.com/paper/2006.10350/) (2020)
- [FALKON: An Optimal Large Scale Kernel Method](https://mlsanity.com/paper/1705.10958/) (2017)
- [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)
- [Optimal Rates for Random Fourier Features](https://mlsanity.com/paper/1506.02155/) (2015)
- [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)
- [Iterative Regularization for Learning with Convex Loss Functions](https://mlsanity.com/paper/1503.08985/) (2015)
- [Spatial Decompositions for Large Scale SVMs](https://mlsanity.com/paper/1612.00374/) (2016)
- [Universal Consistency and Robustness of Localized Support Vector Machines](https://mlsanity.com/paper/1703.06528/) (2017)
- [Total Stability of SVMs and Localized SVMs](https://mlsanity.com/paper/2101.12678/) (2021)
- [Quantitative Robustness of Localized Support Vector Machines](https://mlsanity.com/paper/1903.01334/) (2019)
- [On the Connection between Lp and Risk Consistency and its Implications on Regularized Kernel Methods](https://mlsanity.com/paper/2303.15210/) (2023)

## Abstract (arXiv)

Kernel-based regularized risk minimizers, also called support vector machines (SVMs), are known to possess many desirable properties but suffer from their super-linear computational requirements when dealing with large data sets. This problem can be tackled by using localized SVMs instead, which also offer the additional advantage of being able to apply different hyperparameters to different regions of the input space. In this paper, localized SVMs are analyzed with regards to their consistency. It is proven that they inherit Lp- as well as risk consistency from global SVMs under very weak conditions and even if the regions underlying the localized SVMs are allowed to change as the size of the training data set increases.