2013/02/28 by Andrew Gordon Wilson, Ryan Prescott Adams · 2 citations
Mathematics · Computer Science · #stat.ML #cs.AI #stat.ME
published as International Conference on Machine Learning (ICML), JMLR W&CP 28(3):1067-1075, 2013 · 10 pages, 5 figures, 1 table. Minor edits and titled changed from "Gaussian Process Covariance Kernels for Pattern Discovery and Extrapolation" to "Gaussian Process Kernels for Pattern Discovery and Extrapolation". Appears at the International Conference on Machine Learning (ICML), JMLR W&CP 28(3):1067-1075, 2013
arxiv created 2013/12/31 · arxiv updated 2014/01/03
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 CO2 trends and airline passenger data. We also show that we can reconstruct standard covariances within our framework.