Universal Consistency and Robustness of Localized Support Vector Machines

TL;DR

This paper demonstrates that localized support vector machines are universally consistent and statistically robust, offering a scalable and adaptable approach for kernel-based machine learning on large datasets.

Contribution

It proves the universal consistency and robustness of localized SVMs, extending their theoretical understanding and practical applicability.

Findings

Localized SVMs are universally consistent.

Provides an upper bound for maxbias indicating robustness.

Supports scalable kernel-based learning on large data sets.

Abstract

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.