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1、StatisticalConsistencyofTop-kRankingFenXiaTie-YanLiuHangLiInstituteofAutomationMicrosoftResearchAsiaMicrosoftResearchAsiaChineseAcademyofSciencestyliu@microsoft.comhanglig@microsoft.comfen.xia@ia.ac.cnAbstractThispaperisconcernedwiththeconsistencyanalysison
2、listwiserankingmeth-ods.Amongvariousrankingmethods,thelistwisemethodshavecompetitiveper-formancesonbenchmarkdatasetsandareregardedasoneofthestate-of-the-artapproaches.Mostlistwiserankingmethodsmanagetooptimizerankingonthewholelist(permutation)ofobjects,howe
3、ver,inpracticalapplicationssuchasin-formationretrieval,correctrankingatthetopkpositionsismuchmoreimportant.Thispaperaimstoanalyzewhetherexistinglistwiserankingmethodsarestatisti-callyconsistentinthetop-ksetting.Forthispurpose,wedefineatop-krankingframework,w
4、herethetrueloss(andthustherisks)aredefinedonthebasisoftop-ksubgroupofpermutations.Thisframeworkcanincludethepermutation-levelrankingframeworkproposedinpreviousworkasaspecialcase.Basedonthenewframework,wederivesufficientconditionsforalistwiserankingmethodtobec
5、onsistentwiththetop-ktrueloss,andshowaneffectivewayofmodify-ingthesurrogatelossfunctionsinexistingmethodstosatisfytheseconditions.Experimentalresultsshowthatafterthemodifications,themethodscanworksig-nificantlybetterthantheiroriginalversions.1IntroductionRank
6、ingisthecentralprobleminmanyapplicationsincludinginformationretrieval(IR).Inrecentyears,machinelearningtechnologieshavebeensuccessfullyappliedtoranking,andmanylearningtorankmethodshavebeenproposed,includingthepointwise[12][9][6],pairwise[8][7][2],andlistwis
7、emethods[13][3][16].Empiricalresultsonbenchmarkdatasetshavedemonstratedthatthelistwiserankingmethodshaveverycompetitiverankingperformances[10].Toexplainthehighrankingperformancesofthelistwiserankingmethods,atheoreticalframeworkwasproposedin[16].Intheframewo
8、rk,existinglistwiserankingmethodsareinterpretedasmakinguseofdifferentsurrogatelossfunctionsofthepermutation-level0-1loss.Theoreticalanalysisshowsthatthesesurrogatelossfunctionsareallstatisticallyconsis
