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

TL;DR

This paper introduces a variational inference approach for sparse spectrum Gaussian process approximations, modeling the covariance function as a random variable to better handle complex functions and prevent over-fitting.

Contribution

It proposes a novel variational method that models the covariance as a random variable, improving the approximation of complex functions in Gaussian processes.

Findings

Better capture of complex functions compared to standard methods

Avoids over-fitting in sparse spectrum approximations

Extensible to distributed and stochastic settings

Abstract

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.