Universal Consistency and Robustness of Localized Support Vector Machines
This work addresses scalability issues in kernel-based machine learning for researchers and practitioners, but it appears incremental as it builds on existing localized approaches.
The paper tackles the computational and storage challenges of kernel-based methods on large datasets by analyzing localized support vector machines, showing they are universally consistent and providing an upper bound for maxbias to demonstrate statistical robustness.
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.