Improving the Gaussian Process Sparse Spectrum Approximation by Representing Uncertainty in Frequency Inputs
This work addresses a specific issue in Gaussian process modeling for machine learning practitioners, representing an incremental improvement.
The authors tackled the problem of Gaussian process sparse spectrum approximations overfitting and failing to capture complex functions by introducing a variational inference approach that treats the covariance function as a random variable, resulting in improved performance over standard methods.
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.