# Spectrum Gaussian Processes Based On Tunable Basis Functions

arXiv: https://arxiv.org/abs/2107.06473 · HTML: https://mlsanity.com/paper/2107.06473/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 18 of its 42 references that are in the map.
- First posted on arXiv 14 Jul 2021.

## Builds on (most cited first, 18 of 18)

- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Advances in Variational Inference](https://mlsanity.com/paper/1711.05597/) (2017)
- [Gaussian Process Kernels for Pattern Discovery and Extrapolation](https://mlsanity.com/paper/1302.4245/) (2013)
- [Efficiently Sampling Functions from Gaussian Process Posteriors](https://mlsanity.com/paper/2002.09309/) (2020)
- [Hilbert Space Methods for Reduced-Rank Gaussian Process Regression](https://mlsanity.com/paper/1401.5508/) (2014)
- [Variational Fourier features for Gaussian processes](https://mlsanity.com/paper/1611.06740/) (2016)
- [Understanding Probabilistic Sparse Gaussian Process Approximations](https://mlsanity.com/paper/1606.04820/) (2016)
- [Sparse Gaussian Processes with Spherical Harmonic Features](https://mlsanity.com/paper/2006.16649/) (2020)
- [Optimal Transport Kernels for Sequential and Parallel Neural Architecture Search](https://mlsanity.com/paper/2006.07593/) (2020)
- [Orthogonally Decoupled Variational Gaussian Processes](https://mlsanity.com/paper/1809.08820/) (2018)
- [Gaussian process emulators for computer experiments with inequality constraints](https://mlsanity.com/paper/1606.01265/) (2016)
- [Function-Space Distributions over Kernels](https://mlsanity.com/paper/1910.13565/) (2019)
- [Finite-dimensional Gaussian approximation with linear inequality constraints](https://mlsanity.com/paper/1710.07453/) (2017)
- [Improving the Gaussian Process Sparse Spectrum Approximation by Representing Uncertainty in Frequency Inputs](https://mlsanity.com/paper/1503.02424/) (2015)
- [Know Your Boundaries: Constraining Gaussian Processes by Variational Harmonic Features](https://mlsanity.com/paper/1904.05207/) (2019)
- [Variational Orthogonal Features](https://mlsanity.com/paper/2006.13170/) (2020)
- [Sparse Gaussian Processes via Parametric Families of Compactly-supported Kernels](https://mlsanity.com/paper/2006.03673/) (2020)
- [Sparse Gaussian Process Based On Hat Basis Functions](https://mlsanity.com/paper/2006.08117/) (2020)

## Abstract (arXiv)

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.