Automated Spectral Kernel Learning

TL;DR

This paper introduces a spectral kernel learning framework that creates input- and output-dependent kernels using non-stationary spectral measures, improving kernel methods' adaptability for complex tasks.

Contribution

It proposes a novel spectral kernel learning approach with data-dependent regularization, enhancing kernel flexibility and generalization over traditional stationary kernels.

Findings

The framework outperforms traditional kernels in experiments.

Theoretical error bounds support improved generalization.

Regularization terms enhance learning performance.

Abstract

The generalization performance of kernel methods is largely determined by the kernel, but common kernels are stationary thus input-independent and output-independent, that limits their applications on complicated tasks. In this paper, we propose a powerful and efficient spectral kernel learning framework and learned kernels are dependent on both inputs and outputs, by using non-stationary spectral kernels and flexibly learning the spectral measure from the data. Further, we derive a data-dependent generalization error bound based on Rademacher complexity, which estimates the generalization ability of the learning framework and suggests two regularization terms to improve performance. Extensive experimental results validate the effectiveness of the proposed algorithm and confirm our theoretical results.