A Closer Look at Covering Number Bounds for Gaussian Kernels

TL;DR

This paper derives new bounds on the covering numbers of Gaussian RKHS, emphasizing explicit constants and parameter dependencies, which are crucial for understanding the complexity of Gaussian kernel methods.

Contribution

It provides novel bounds on Gaussian RKHS covering numbers with explicit constants, improving understanding of parameter influences compared to prior work.

Findings

Explicit bounds on Gaussian RKHS covering numbers.

Analysis of how kernel bandwidth affects complexity.

Insights into the role of space size and dimension.

Abstract

We establish some new bounds on the log-covering numbers of (anisotropic) Gaussian reproducing kernel Hilbert spaces. Unlike previous results in this direction we focus on small explicit constants and their dependency on crucial parameters such as the kernel bandwidth and the size and dimension of the underlying space.