资源描述：
《Gaussian_Processes_For_Machine_Learning_toolbox.pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。
1、JournalofMachineLearningResearch11(2010)3011-3015Submitted8/10;Revised9/10;Published11/10GaussianProcessesforMachineLearning(GPML)ToolboxCarlEdwardRasmussen∗CER54@CAM.AC.UKDepartmentofEngineeringUniversityofCambridgeTrumpingtonStreetCambridge,CB21PZ,UKH
2、annesNickischHN@TUE.MPG.DEMaxPlanckInstituteforBiologicalCyberneticsSpemannstraße3872076Tubingen,Germany¨Editor:SorenSonnenburg¨AbstractTheGPMLtoolboxprovidesawiderangeoffunctionalityforGaussianprocess(GP)inferenceandprediction.GPsarespecifiedbymeanandco
3、variancefunctions;weofferalibraryofsimplemeanandcovariancefunctionsandmechanismstocomposemorecomplexones.Severallikeli-hoodfunctionsaresupportedincludingGaussianandheavy-tailedforregressionaswellasotherssuitableforclassification.Finally,arangeofinference
4、methodsisprovided,includingexactandvariationalinference,ExpectationPropagation,andLaplace'smethoddealingwithnon-GaussianlikelihoodsandFITCfordealingwithlargeregressiontasks.Keywords:Gaussianprocesses,nonparametricBayes,probabilisticregressionandclassific
5、ationGaussianprocesses(GPs)(RasmussenandWilliams,2006)haveconvenientpropertiesformanymodellingtasksinmachinelearningandstatistics.Theycanbeusedtospecifydistributionsoverfunctionswithouthavingtocommittoaspecificfunctionalform.Applicationsrangefromregres-s
6、ionoverclassificationtoreinforcementlearning,spatialmodels,survivalandothertimeseries1models.PredictionsofGPmodelscomewithanaturalconfidencemeasure:predictiveerror-bars.Althoughtheimplementationofthebasicprinciplesinthesimplestcaseisstraightforward,variou
7、scomplicatingfeaturesareoftendesiredinpractice.Forexample,aGPisdeterminedbyameanfunctionandacovariancefunction,butthesefunctionsaremostlydifficulttospecifyfullyapriori,andtypicallytheyaregivenintermsofhyperparameters,thatis,parameterswhichhavetobeinferre
8、d.Anothersourceofdifficultyisthelikelihoodfunction.ForGaussianlikelihoods,in-ferenceisanalyticallytractable;however,inmanytasks,Gaussianlikelihoodsarenotappropriate,andapproximateinferencemethodssuchasExpectationPropagation(EP)(Mi
