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

Yarin Gal and Richard E. Turner

Published in: Proceedings of The 32nd International Conference on Machine Learning,

Standard sparse pseudo-input approximations to the Gaussian process (GP) cannot handle com- plex 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 distribu- tion 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 stochas- tic domains. Our approximation captures com- plex functions better than standard approaches and avoids over-fitting.

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