# Universal Consistency and Robustness of Localized Support Vector Machines

arXiv: https://arxiv.org/abs/1703.06528 · HTML: https://mlsanity.com/paper/1703.06528/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Mar 2017.

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

- [Robust Kernel-based Distribution Regression](https://mlsanity.com/paper/2104.10637/) (2021)
- [ParK: Sound and Efficient Kernel Ridge Regression by Feature Space Partitions](https://mlsanity.com/paper/2106.12231/) (2021)
- [Total Stability of SVMs and Localized SVMs](https://mlsanity.com/paper/2101.12678/) (2021)
- [Lp- and Risk Consistency of Localized SVMs](https://mlsanity.com/paper/2305.09385/) (2023)

## Abstract (arXiv)

The massive amount of available data potentially used to discover patters in machine learning is a challenge for kernel based algorithms with respect to runtime and storage capacities. Local approaches might help to relieve these issues. From a statistical point of view local approaches allow additionally to deal with different structures in the data in different ways. This paper analyses properties of localized kernel based, non-parametric statistical machine learning methods, in particular of support vector machines (SVMs) and methods close to them. We will show there that locally learnt kernel methods are universal consistent. Furthermore, we give an upper bound for the maxbias in order to show statistical robustness of the proposed method.