Explicit Universal and Approximate-Universal Kernels on Compact Metric Spaces

TL;DR

This paper presents explicit constructions of universal and approximately universal kernels on compact metric spaces, enhancing the theoretical foundation and practical applicability of kernel methods in machine learning.

Contribution

It introduces explicit universal kernels on compact metric spaces and proposes a new notion of approximate universality with tractable kernel constructions.

Findings

Explicit universal kernels on compact metric spaces are constructed.

A new notion of approximate universality is introduced.

Tractable kernels that are approximately universal are developed.

Abstract

Universal kernels, whose Reproducing Kernel Hilbert Space is dense in the space of continuous functions are of great practical and theoretical interest. In this paper, we introduce an explicit construction of universal kernels on compact metric spaces. We also introduce a notion of approximate universality, and construct tractable kernels that are approximately universal.