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



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Gal, Yarin 
Turner, Richard 


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.


This is the final version of the article. It first appeared at


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Journal of Machine Learning Research

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Microtome Publishing

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YG is supported by the Google European Fellowship in Machine Learning. Funding was provided by the EPSRC (grant numbers EP/G050821/1 and EP/L000776/1) and Google (R.E.T.).