Nonparamater_Bayesian_Model

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1、HierarchicalBayesianNonparametricModelswithApplicationsYeeWhyeTehGatsbyComputationalNeuroscienceUnitUniversityCollegeLondon17QueenSquareLondonWC1N3AR,UnitedKingdomMichaelI.JordanDepartmentofStatisticsDepartmentofElectricalEngineeringandComputerScienceUniversityofCalifornia,BerkeleyBerkeley,CA94

2、720,USAFebruary14,2009AbstractHierarchicalmodelingisafundamentalconceptinBayesianstatistics.Thebasicideaisthatparametersareendowedwithdistributionswhichmaythemselvesintroducenewparameters,andthisconstructionrecurses.InthisreviewwediscusstheroleofhierarchicalmodelinginBayesiannon-parametrics,foc

3、usingonmodelsinwhichtheinnite-dimensionalparame-tersaretreatedhierarchically.Forexample,weconsideramodelinwhichthebasemeasureforaDirichletprocessisitselftreatedasadrawfromanotherDirichletprocess.ThisyieldsanaturalrecursionthatwerefertoasahierarchicalDirichletprocess.Wealsodiscusshierarchiesbas

4、edonthePitman-Yorprocessandoncompletelyrandomprocesses.Wedemonstratethevalueofthesehierarchicalconstructionsinawiderangeofpracticalapplications,inproblemsincomputationalbiology,computervisionandnaturallanguageprocessing.1IntroductionHierarchicalmodelingisafundamentalconceptinBayesianstatistics.

5、Thebasicideaisthatparametersareendowedwithdistributionswhichmaythemselvesintroducenewparameters,andthisconstructionrecurses.Acommonmotifinhierarchicalmodelingisthatoftheconditionallyindependenthierarchy,inwhichasetofparametersarecoupledbymakingtheirdistributionsdepend1onasharedunderlyingparamet

6、er.Thesedistributionsareoftentakentobeidentical,basedonanassertionofexchangeabilityandanappealtodeFinetti'stheorem.Hierarchieshelptounifystatistics,providingaBayesianinterpretationoffrequentistconceptssuchasshrinkageandrandomeects.Hierarchiesalsoprovidewaystospecifynon-standarddistributionalfo

7、rms,obtainedasintegralsoverunderlyingparameters.Theyplayaroleincomputationalpracticeintheguiseofvariableaugmentation.Theseadvantagesarewellappreciatedintheworldofparametricmodeling,andfewBayesianparametricmodelersfailtomakeuseofso