Spectrum Gaussian Processes Based On Tunable Basis Functions

TL;DR

This paper introduces a novel tunable basis function inspired by quantum physics for Gaussian processes, improving spectral approximation and variational learning, especially with poorly chosen kernels.

Contribution

It proposes a new local, bounded, tunable basis function for Gaussian processes, differing from traditional orthonormal bases, enhancing approximation flexibility.

Findings

Achieves comparable or better performance than state-of-the-art methods.

Effective with poorly chosen kernel functions.

Demonstrated on open-source datasets.

Abstract

Spectral approximation and variational inducing learning for the Gaussian process are two popular methods to reduce computational complexity. However, in previous research, those methods always tend to adopt the orthonormal basis functions, such as eigenvectors in the Hilbert space, in the spectrum method, or decoupled orthogonal components in the variational framework. In this paper, inspired by quantum physics, we introduce a novel basis function, which is tunable, local and bounded, to approximate the kernel function in the Gaussian process. There are two adjustable parameters in these functions, which control their orthogonality to each other and limit their boundedness. And we conduct extensive experiments on open-source datasets to testify its performance. Compared to several state-of-the-art methods, it turns out that the proposed method can obtain satisfactory or even better results, especially with poorly chosen kernel functions.