Transcription of Gaussian Processes for Regression: A Quick Introduction
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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).N otquiteenoughflexibilitythough:thedataar eoftennoisyaswell, :(2)somethingwhichshouldlookfamiliartoth osewho ,wetakethenovelapproachoffoldingthenoise into,bywriting(3)whereistheKroneckerdelt afunction.
the zero vector representing the mean of the multivariate Gaussian distribution in (6) can be replaced with functions of . Third, in addition to their use in regression, GPs are applicableto integration,globaloptimization, mixture-of-expertsmodels,unsuper-vised learning models, and more — see Chapter 9 of Rasmussen and Williams (2006).
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