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shrink globally act locally sparse bayesian regularization and prediction bayesian models for sparse regression

shrink globally act locally sparse bayesian regularization and prediction bayesian models for sparse regression

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页数：45页

时间：2018-02-10

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1、ShrinkGlobally,ActLocally:SparseBayesianRegularizationandPrediction*UniversityPressScholarshipOnlineOxfordScholarshipOnlineBayesianStatistics9JoséM.Bernardo,M.J.Bayarri,JamesO.Berger,A.P.Dawid,DavidHeckerman,AdrianF.M.Smith,andMikeWestPrintpublicationdate:2011PrintISBN-13:9780199694587Publishedt

2、oOxfordScholarshipOnline:January2012DOI:10.1093/acprof:oso/9780199694587.001.0001ShrinkGlobally,ActLocally:SparseBayesianRegularizationandPrediction*NicholasG.PolsonJamesG.ScottDOI:10.1093/acprof:oso/9780199694587.003.0017AbstractandKeywordsWestudytheclassicproblemofchoosingapriordistributionfor

3、alocationparameterβ=(β1,…,βp)aspgrowslarge.First,westudythestandard“global‐localshrinkage”approach,basedonscalemixturesofnormals.Twotheoremsarepresentedwhichcharacterizecertaindesirablepropertiesofshrinkagepriorsforsparseproblems.Next,wereviewsomerecentresultsshowinghowLévyprocessescanbeusedtoge

4、nerateinfinite‐dimensionalversionsofstandardnormalscale‐mixturepriors,alongwithnewpriorsthathaveyettobeseriouslystudiedintheliterature.Thisapproachprovidesanintuitiveframeworkbothforgeneratingnewregularizationpenaltiesandshrinkagerules,andforperformingasymptoticanalysisonexistingmodels.Keywords:

5、LévyProcesses,Shrinkage,SparsityPage1of45ShrinkGlobally,ActLocally:SparseBayesianRegularizationandPrediction*SummaryWestudytheclassicproblemofchoosingapriordistributionforalocationparameterβ=(β1,…,βp)aspgrowslarge.First,westudythestandard“global‐localshrinkage”approach,basedonscalemixturesofnorm

6、als.Twotheoremsarepresentedwhichcharacterizecertaindesirablepropertiesofshrinkagepriorsforsparseproblems.Next,wereviewsomerecentresultsshowinghowLévyprocessescanbeusedtogenerateinfinite‐dimensionalversionsofstandardnormalscale‐mixturepriors,alongwithnewpriorsthathaveyettobeseriouslystudiedinthel

7、iterature.Thisapproachprovidesanintuitiveframeworkbothforgeneratingnewregularizationpenaltiesandshrinkagerules,andforperformingasymptoticanalysisonexistingmodels.KeywordsandPhrases:LÉVYPROCESSES;SHRINKAGE;SPARSITY1.One‐Group

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