[8] Boosting Algorithms Regularization， prediction and model fitting by Peter B&amp#252;hlmann and Torsten Hothorn.pdf

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1、StatisticalScience2007,Vol.22,No.4,477505DOI:10.1214/07-STS242©InstituteofMathematicalStatistics,2007BoostingAlgorithms:Regularization,PredictionandModelFittingPeterBühlmannandTorstenHothornAbstract.Wepresentastatisticalperspectiveonboosting.Specialempha-sisis

2、giventoestimatingpotentiallycomplexparametricornonparametricmodels,includinggeneralizedlinearandadditivemodelsaswellasregres-sionmodelsforsurvivalanalysis.Conceptsofdegreesoffreedomandcor-respondingAkaikeorBayesianinformationcriteria,particularlyusefulforregul

3、arizationandvariableselectioninhigh-dimensionalcovariatespaces,arediscussedaswell.Thepracticalaspectsofboostingproceduresforfittingstatisticalmod-elsareillustratedbymeansofthededicatedopen-sourcesoftwarepackagemboost.Thispackageimplementsfunctionswhichcanbeused

4、formodelfit-ting,predictionandvariableselection.Itisflexible,allowingfortheimple-mentationofnewboostingalgorithmsoptimizinguser-specifiedlossfunc-tions.Keywordsandphrases:Generalizedlinearmodels,generalizedadditivemodels,gradientboosting,survivalanalysis,variable

5、selection,software.1.INTRODUCTIONgradientdescentalgorithminfunctionspace,inspiredbynumericaloptimizationandstatisticalestimation.FreundandSchapiresAdaBoostalgorithmforclas-Moreover,Friedman,HastieandTibshirani[33]laidsification[2931]hasattractedmuchattentionint

6、heoutfurtherimportantfoundationswhichlinkedAda-machinelearningcommunity(cf.[76],andtherefer-Boostandotherboostingalgorithmstotheframeworkencestherein)aswellasinrelatedareasinstatisticsofstatisticalestimationandadditivebasisexpansion.[15,16,33].Variousversionso

7、ftheAdaBoostalgo-Intheirterminology,boostingisrepresentedasstage-rithmhaveproventobeverycompetitiveintermsofwise,additivemodeling:thewordadditivedoesnotpredictionaccuracyinavarietyofapplications.Boost-implyamodelfitwhichisadditiveinthecovariatesingmethodshavebe

8、enoriginallyproposedasensem-(seeourSection4),butreferstothefactthatboost-blemethods(seeSection1.1),whichrelyontheprin-ingisanadditive(infact,alinear)combinationofcipleofgeneratingm