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1、GaussianProcessesforPredictionTechnicalReportPARG-07-01MichaelOsborneRoboticsResearchGroupDepartmentofEngineeringScienceUniversityofOxfordOctober4,2007GaussianProcessesforPredictionSummaryWeproposeapowerfulpredictionalgorithmbuiltuponGaussianprocesses(GPs).Theyareparticu
2、larlyusefulfortheir?exibility,facilitatingaccuratepredictionevenintheabsenceofstrongphysicalmodels.GPsfurtherallowustoworkwithinacompleteBayesianprobabilisticframework.Assuch,weshowhowthehyperparametersofoursystemcanbemarginalisedbyuseofBayesianMonteCarlo,aprincipledmeth
3、odofapproximateintegration.WeemploytheerrorbarsofourGP’spredictionsasameanstoselectonlythemostinformativedatatostore.ThisallowsustointroduceaniterativeformulationoftheGPtogiveadynamic,on-linealgorithm.Wealsoshowhowourerrorbarscanbeusedtoperformactivedataselection,allowin
4、gtheGPtoselectwhereandwhenitshouldnexttakeameasurement.Wedemonstratehowourmethodscanbeappliedtomulti-sensorpredictionproblemswheredatamaybemissing,delayedand/orcorrelated.Inparticular,wepresentarealnetworkofweathersensorsasatestbedforouralgorithm.Contents1Introduction12P
5、robabilityTheory32.1Foundations..........................................32.2Second-orderprobability...................................63GaussianProcesses133.1Introduction..........................................133.2ParametersandHyperparameters.........................
6、.....143.3ModifyingCovarianceFunctions...............................163.4CorrelatedInputsandOutputs...............................163.5Implementation........................................193.6MarginalisingHyperparameters...............................213.7BayesianMont
7、eCarlo....................................253.8MarginalisingRevisited...................................294Iterativemethods334.1GPUpdating.........................................334.2IterativeMarginalisation...................................344.3DiscardingData.........
8、..............................374.4ActiveDataSelection....................................395WeatherSen
