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Gaussianprocessisfullyspecifiedbyitsmeanfunctionm(x)andcovariancefunctionk(x,x0)Usedinspatialstatistics,geostatistics(kriging),meteorologyOnline ISBNBooks>GaussianProcessesforMachinGaussianProcessesforMachineLearning.CarlE.Rasmussen,Abstract.Wefocusonunderstandingtheroleof thestochasticandhowitisusedtodefineadistributionoverGaussianProcessesforMachineLearningGaussianprocessesarenotnew!AGaussianprocessisa stochasticprocessspecifiedbyitsmeanandcovarianceRasmussen,CarlEdwardChapterIntroductionPublishedComputerScience,MathematicspInthis bookwewillbeconcernedwithsupervisedlearning,whichistheproblemoflearninginput-outputChrisWilliamsANCGaussianProcessesforMachineLearning Keyobservation:AGaussianprocessisanaturalgeneralizationfromvectorstofunctions:f(x)∼GP(m(x),k(x,x0))GaussianProcessesforMachineLearningcm GaussianprocessesformachinelearningCarlEdwardRasmussen,ChristopherKIWilliamsCorpusIDGaussianProcessesforMachineLearningCarlEdward RasmussenDefinitionAGaussianProcessisacollectionofrandomvariables,anyfinitenumberofwhichhave(consistent)jointGaussiandistributions.CarlWhy GaussianProcesses.TLDRGaussianprocesses(GPs)(RasmussenandWilliams,)haveconvenientpropertiesformanymodellingtasksinmachinelearningand statisticsMITPressThebookdealswiththesupervised-learningproblemforbothregressionandclassification,andincludesdetailedalgorithmsThemainfocus ofthebookistopresentclearlyandconciselyanoverviewofthemainideasofGaussianprocessesinamachinelearningcontext (Adaptivecomputationand machinelearning)IncludesbibliographicalreferencesandindexesGPshavereceivedincreasedattentioninthemachine-learningcommunityoverthepastade,and thisbookprovidesalong-neededsystematicandunifiedtreatmentoftheoreticalandpracticalaspectsofGPsinmachinelearningDefinitionAGaussianProcessisa collectionofrandomvariables,anyfinitenumberofwhichhave(consistent)jointGaussiandistributionsCarlERasmussen,ChristopherKIWilliamsThisisa naturalgeneralizationoftheGaussiandistributionwhosemeanandcovarianceisavectorandWegiveabasicintroductiontoGaussianProcessmodels.Whyare GPsnotusedmoreoften?Wehavealsocoveredawiderangeofconnectionstoexistingmodelsintheliterature,andcoverapproximateinferenceforfaster practicalalgorithmsGaussianProcessesDefinition:AGaussianProcessisacollectionofrandomvariablesanyfinitenumberofwhichhave(consistent)joint Gaussiandistributionscomputational[PDF]GaussianProcessesforMachineLearningSemanticScholarISBNXGaussianprocesses DataprocessingMachine learning MathematicalmodelsThetreatmentiscomprehensiveandself-contained,targetedatresearchersandstudentsinmachinelearningandappliedstatistics TheycanbeusedtoComputingandProcessingTheycanbeusedtospecifydistributionsoverfunctionswithouthavingtocommittoaspecificfunctionalform BookAbstract:Gaussianprocesses(GPs)provideaprincipled,practical,probabilisticapproachtolearninginkernelmachinesGaussianProcessesAGaussian processes(GPs)(RasmussenandWilliams,)haveconvenientpropertiesformanymodellingtasksinmachinelearningandstatistics.