Gaussian processes are rich distributions over functions, which provide a Bayesian nonparametric approach to smoothing and interpolation. We introduce simple closed form kernels that can be used with Gaussian processes to discover patterns and enable extrapolation. These kernels are derived by modelling a spectral density -the Fourier transform of a kernel -with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian process inference remains simple and analytic. We demonstrate the proposed kernels by discovering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO 2 trends and airline passenger data. We also show that it is possible to reconstruct several popular standard covariances within our framework.
To allow for highly flexible kernel learning, REF proposed spectral mixture kernels, derived by modelling a spectral density by a scale-location mixture of Gaussians.
Gaussian Process Kernels for Pattern Discovery and Extrapolation
International Conference on Machine Learning (ICML), JMLR W&CP 28(3):1067-1075, 2013
Mathematics Computer Science