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1、Classi cationandRegressionTrees36-350,DataMining6November2009Contents1PredictionTrees12RegressionTrees42.1Example:CaliforniaRealEstateAgain...............42.2RegressionTreeFitting.......................72.2.1Cross-ValidationandPruninginR.............132.3U
2、ncertaintyinRegressionTrees...................143Classi cationTrees183.1MeasuringInformation........................193.2MakingPredictions..........................203.3MeasuringError...........................203.3.1Misclassi cationRate...................
3、.203.3.2AverageLoss.........................213.3.3LikelihoodandCross-Entropy................213.3.4Neyman-PearsonApproach.................234FurtherReading245Exercises24Reading:PrinciplesofDataMining,sections10.5and5.2(inthatorder);Berk,chapter3Havingbuil
4、tupincreasinglycomplicatedmodelsforregression,I'llnowswitchgearsandintroduceaclassofnonlinearpredictivemodelwhichat rstseemstoosimpletopossiblework,namelypredictiontrees.Thesehavetwovarieties,regressiontreesandclassi cationtrees.1PredictionTreesThebasicide
5、aisverysimple.WewanttopredictaresponseorclassYfrominputsX1;X2;:::Xp.Wedothisbygrowingabinarytree.Ateachinternal1nodeinthetree,weapplyatesttooneoftheinputs,sayXi.Dependingontheoutcomeofthetest,wegotoeithertheleftortherightsub-branchofthetree.Eventuallywecom
6、etoaleafnode,wherewemakeaprediction.Thispredictionaggregatesoraveragesallthetrainingdatapointswhichreachthatleaf.Figure1shouldhelpclarifythis.Whydothis?Predictorslikelinearorpolynomialregressionareglobalmodels,whereasinglepredictiveformulaissupposedtoholdo
7、vertheentiredataspace.Whenthedatahaslotsoffeatureswhichinteractincomplicated,nonlinearways,assemblingasingleglobalmodelcanbeverydicult,andhope-lesslyconfusingwhenyoudosucceed.Someofthenon-parametricsmootherstryto tmodelslocallyandthenpastethemtogether,but
8、againtheycanbehardtointerpret.(Additivemodelsareatleastprettyeasytograsp.)Analternativeapproachtononlinearregressionistosub-divide,orparti-tion,thespaceintosmallerregions,wheretheinteractionsaremoremanage-abl
