Gaussian Processes for Prediction.pdf

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1、GaussianProcessesforPredictionTechnicalReportPARG-07-01MichaelOsborneRoboticsResearchGroupDepartmentofEngineeringScienceUniversityofOxfordOctober4,2007GaussianProcessesforPredictionSummaryWeproposeapowerfulpredictionalgorithmbuiltuponGaussianprocesses(GPs).Theyareparticu

2、larlyusefulfortheirflexibility,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