Wilson, Andrew GordonAdams, Ryan Prescott2013-11-252013Andrew Gordon Wilson; Ryan Prescott Adams. 2013. Gaussian process kernels for pattern discovery and extrapolation. Journal of Machine Learning Research 28, no. 3: 1067-1075.1532-4435http://nrs.harvard.edu/urn-3:HUL.InstRepos:11337457Gaussian 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 modeling 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 CO2 trends and airline passenger data. We also show that it is possible to reconstruct several popular standard covariances within our framework.en-USConference Paper2013-08-08Andrew Gordon Wilson; Ryan Prescott Adams2013-11-26