# Improving the Gaussian Process Sparse Spectrum Approximation by Representing Uncertainty in Frequency Inputs

arXiv: https://arxiv.org/abs/1503.02424 · HTML: https://mlsanity.com/paper/1503.02424/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Mar 2015.

## Built on by (most cited first, 11 of 11)

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- [On Connecting Deep Trigonometric Networks with Deep Gaussian Processes: Covariance, Expressivity, and Neural Tangent Kernel](https://mlsanity.com/paper/2203.07411/) (2022)
- [Adaptive RKHS Fourier Features for Compositional Gaussian Process Models](https://mlsanity.com/paper/2407.01856/) (2024)
- [Spectrum Gaussian Processes Based On Tunable Basis Functions](https://mlsanity.com/paper/2107.06473/) (2021)
- [How Good are Low-Rank Approximations in Gaussian Process Regression?](https://mlsanity.com/paper/2112.06410/) (2021)
- [Modeling Disagreement in Automatic Data Labelling for Semi-Supervised Learning in Clinical Natural Language Processing](https://mlsanity.com/paper/2205.14761/) (2022)

## Abstract (arXiv)

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle complex functions well. Sparse spectrum alternatives attempt to answer this but are known to over-fit. We suggest the use of variational inference for the sparse spectrum approximation to avoid both issues. We model the covariance function with a finite Fourier series approximation and treat it as a random variable. The random covariance function has a posterior, on which a variational distribution is placed. The variational distribution transforms the random covariance function to fit the data. We study the properties of our approximate inference, compare it to alternative ones, and extend it to the distributed and stochastic domains. Our approximation captures complex functions better than standard approaches and avoids over-fitting.