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Gaussian Processes for Regression: A Quick Introduction

Speak , ,GPRisaless parametric ,it snotcompletelyfree-form,andifwe reunwillingtomakeevenbasicassumptionsabo ut,thenmoregen-eraltechniquesshouldbecon sidered,includingthoseunderpinnedbythepr incipleofmaximumentropy;Chapter6ofSiviaa ndSkilling(2006)offersanintroduction. 1 2 1 :Givensixnoisydatapoints(errorbarsareind icatedwithverticallines), (GPs) , ,theobservationsinanarbitrarydataset,,ca nalwaysbeimaginedasasinglepointsampledfr omsomemultivariate(-variate)Gaussiandist ri-bution, ,workingbackwards, ,it ,.Apopularchoiceisthe squaredexponential ,(1)wherethemaximumallowablecovarianceis definedas ,thenapproachesthismaximum, :forourfunctiontolooksmooth, ,wehaveinstead, see ,forexample,duringinterpolationatnewvalu es, ,,sothereismuchflexibilitybuiltinto(1).

Data Analysis: A Bayesian Tutorial (second ed.). Oxford Science Publications. APPENDIX Imagine a data sample taken from some multivariateGaussian distributionwith zero mean and a covariance given by matrix . Now decompose arbitrarily into two consecutive subvectors and — in other words, writing would be the same as writing (13)

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