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Classification and Regression by randomForest

,December200218 ClassificationandRegressionbyrandomFores tAndyLiawandMatthewWienerIntroductionRec entlytherehasbeenalotofinterestin ensem-blelearning (see, ,Shapireetal.,1998)andbaggingBreiman(199 6) , , ,successivetreesdonotdependonearliertree s , (2001)proposedrandomforests, , , , ,includingdiscriminantanalysis,supportve ctorma-chinesandneuralnetworks,andisrobu stagainstoverfitting(Breiman,2001).Inadd ition,itisveryuser-friendlyinthesensetha tithasonlytwoparam-eters(thenumberofvari ablesintherandomsubsetateachnodeandthenu mberoftreesintheforest), ( ). (forbothclassificationandregression) ,growanun-prunedclassificationorregressi ontree,withthefollowingmodification:atea chnode,ratherthanchoosingthebestsplitamo ngallpredic-tors,randomlysamplemtryofthe predictorsandchoosethebestsplitfromamong thosevariables.

structed, random forest, with the default m try, we were able to clearly identify the only two informa-tive variables and totally ignore the other 998 noise variables. A regression example We use the Boston Housing data (available in the MASSpackage)asanexampleforregressionbyran-dom forest. Note a few differences between classifi-

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