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1、AnalysisofCrowdsourcedSamplingStrategiesforHodgeRankwithSparseRandomGraphsBraxtonOstinga,,JiechaoXiongc,QianqianXub,YuanYaoc,aDepartmentofMathematics,UniversityofUtah,SaltLakeCity,UT84112USAbBICMR,PekingUniversity,Beijing100871,ChinacSchoolofMathematicalSciences,BICMR-LMAM-LMEQF-LMP,Pek
2、ingUniversity,Beijing100871,ChinaAbstractCrowdsourcingplatformsarenowextensivelyusedforconductingsubjectivepairwisecomparisonstudies.Inthissetting,apairwisecomparisondatasetistypicallygatheredviarandomsampling,eitherwithorwithoutreplacement.Inthispaper,weusetoolsfromrandomgraphtheorytoana
3、lyzethesetworandomsamplingmethodsfortheHodgeRankestimator.UsingtheFiedlervalueofthegraphasameasurementforestimatorstability(informativeness),weprovideanewestimateoftheFiedlervalueforthesetworandomgraphmodels.Intheasymptoticlimitasthenumberofverticestendstoin nity,weprovethevalidityofthees
4、timate.Basedonour ndings,forasmallnumberofitemstobecompared,werecommendatwo-stagesamplingstrategywhereagreedysamplingmethodisusedinitiallyandrandomsamplingwithoutreplacementisusedinthesecondstage.Whenalargenumberofitemsistobecompared,werecommendrandomsamplingwithreplacementasthisiscomputa
5、tionallyinexpensiveandtriviallyparallelizable.Experimentsonsyntheticandreal-worlddatasetssupportouranalysis.Keywords:Crowdsourcing,PairedComparison,AlgebraicConnectivity,arXiv:1503.00164v2[stat.ML]21Mar2016Erd•os-RenyiRandomGraphCorrespondingauthor.Emailaddresses:osting@math.utah.edu(Br
6、axtonOsting),xiongjiechao@pku.edu.cn(JiechaoXiong),xuqianqian@math.pku.edu.cn(QianqianXu),yuany@math.pku.edu.cn(YuanYao)PreprintsubmittedtoAppliedandComputationalHarmonicAnalysisMarch12,20181.IntroductionWiththeadventofubiquitousinternetaccessandthegrowthofcrowd-sourcingplatforms(e.g.,MTu
7、rk,InnoCentive,CrowdFlower,CrowdRank,andAllOurIdeas),thecrowdsourcingstrategyisnowemployedbyavarietyofcommunities.Crowdsourcingenablesresearcherstoconductsocialexper-imentsonaheterogenoussetofparticipantsandatalowereconomiccostthanconventionallaboratorystudies.Forex
