Transcription of Greedy Function Approximation: A Gradient Boosting …
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Greedy Function Approximation: A Gradient Boosting …
February24,1999 AbstractFunctionapproximationisviewedfro mtheperspectiveofnumericaloptimizationin functionspace, { {descent\ Boosting "paradigmisdevelopedfor additiveexpansionsbasedonany cal-gorithmsarepresentedforleast{squares ,least{absolute{deviation,andHuber{Mloss func-tionsforregression,andmulti{classlo gisticlikelihoodforclassi ,andtoolsforinterpretingsuch\TreeBoost" ,highlyrobust,interpretableproceduresfor regressionandclassi cation, ,andFriedman,Hastie, \output"or\re-sponse"variableyandasetofr andom\input"or\explanatory"variablesx=fx 1; ; \training"samplefyi;xigN1ofknown(y;x){va lues,thegoalisto ndafunctionF (x)thatmapsxtoy,suchthatoverthejointdist ributionofall(y;x){values,theexpectedval ueofsomespeci edlossfunction (y;F(x))isminimizedF (x)=argminF(x)Ey;x (y;F(x))=argminF(x)Ex[Ey( (y;F(x))jx]:(1)Frequentlyemployedlossfun ctio)}}}}}}}}}
O CMIS, Lo c k ed Bag 17, North Ryde NSW 1670; jhf@stat.stanford.edu 1. 1987), MARS (F riedman 1991), w a v elets (Donoho 1993), and supp ort v ector mac hines (V apnik 1995). Of sp ecial in terest here is the case where these functions are c haracterized b y small decision trees, suc h as those pro duced b y CAR T TM (Breiman, F riedman ...
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