Gaussian process kernels for pattern discovery and extrapolation supplementary material and code. 2013. http://mlg.eng. cam.ac.uk/andrew/smkernelsupp.pdf

Gaussian processes are rich distributions over functions, which provide a Bayesian nonpara-metric approach to smoothing and interpola-tion. We introduce simple closed form ker-nels that can be used with Gaussian pro-cesses to discover patterns and enable extrap-olation. These kernels are derived by mod-elling a spectral density – the Fourier trans-form of a kernel – with a Gaussian mixture. The proposed kernels support a broad class of stationary covariances, but Gaussian pro-cess inference remains simple and analytic. We demonstrate the proposed kernels by dis-covering patterns and performing long range extrapolation on synthetic examples, as well as atmospheric CO2 trends and airline pas-senger data. We also show that it is possible to reconstruct several popular standard co-variances within our framework. 1