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AGentleIntroductiontoGradientBoosting

ChengLi

chengli@ccs.neu.edu

CollegeofComputeran dIn formationScience

NortheasternUniversity

GradientBoosting

apo werfulmachinelearningal gorithm itcan do regression classification ranking wonTrac k1oftheYahooLea rni ngt oRankCha llenge

Ourimplem entationofGradientBoostingisavailableat

https://github.com/cheng-li/pyramid

Outlineof theTuto rial

1WhatisGradie ntBoost ing

2Abriefhistory

3GradientBoostingforregress ion

4GradientBoostingforclass ification

5Ade moofGradientB oost ing

6RelationshipbetweenAdaboostandGrad ientBoosting

7Whyit works

Note:Th istutorialfo cusesontheintuition.Foraf ormal treatment,see[Friedman,2001]

WhatisG radientBo osting

GradientBoosting=Gradie ntDescent+Boosting

Adaboost

Figure:AdaBoost.Source:Figure1.1of[ SchapireandFreund, 2012]

WhatisG radientBo osting

GradientBoosting=Gradie ntDescent+Boosting

Adaboost

Figure:AdaBoost.Source:Figure1.1of[ SchapireandFreund, 2012]

Fitanadditi vemo del(ensemble)

t t h t (x)inaforward stage-wisemanner. Ineach stage,introdu ceaweaklearner tocompensatethe shortcomingsofexistingweaklearn ers . InAdab oost,"shortcomings"areidentifiedbyhigh-weightdata points.

WhatisG radientBo osting

GradientBoosting=Gradie ntDescent+Boosting

Adaboost

H(x)= t t h t (x) Figure:AdaBoost.Source:Figure1.2of[ SchapireandFreund, 2012]

WhatisG radientBo osting

GradientBoosting=Gradie ntDescent+Boosting

GradientBoosting

Fitanadditi vemo del(ensemble)

t t h t (x)inaforward stage-wisemanner. Ineach stage,introdu ceaweaklearner tocompensatethe shortcomingsofexistingweaklearn ers . InGrad ientBoosting,"shortcomings"a reidentifiedby gradients. Recallthat,inAdabo ost,"shortcomings" areide ntifiedby high-weightdatapoints. Bothhigh-we ightdatapointsandgradientstel lushowto improveourmodel.

WhatisG radientBo osting

Whyandhow didresear chersinv entGradie ntBoosting?

ABriefHistoryofGradientBoosting

InventAdaboost,thefi rstsuccessfulboostingalgo rithm [Freundetal.,1996,Freund andSch apire,1997] FormulateAdaboostasgradientd escentwithaspeciallos s function[Breimanetal.,1998,Breiman,1999] GeneralizeAdaboosttoGradientBo ostinginordertohandle ava rietyoflossfunctions [Friedmanetal.,2000,Friedman,2001]

GradientBoostingforRegr ession

GradientBoostingforDi

erentProblem s Di culty: regression===>classification===>ranking

GradientBoostingforRegr ession

Let'splayagame.. .

Youaregi ven(x

1 ,y 1 ),(x 2 ,y 2 ),...,(x n ,y n ),andt het askistofi ta modelF(x)to minimi zesquareloss. Supposeyourfriendwa ntstohelp youandgivesyouamodel F. Youchec khismodelandfin dthemodel isgoodbutnotperf ect.

Therearesomemist akes:F(x

1 )=0.8,wh iley 1 =0.9,an d F(x 2 )=1.4whiley 2 =1.3...Howcan youimprovet hismodel ?

GradientBoostingforRegr ession

Let'splayagame.. .

Youaregi ven(x

1 ,y 1 ),(x 2 ,y 2 ),...,(x n ,y n ),andt het askistofi ta modelF(x)to minimi zesquareloss. Supposeyourfriendwa ntstohelp youandgivesyouamodel F. Youchec khismodelandfin dthemodel isgoodbutnotperf ect.

Therearesomemist akes:F(x

1 )=0.8,wh iley 1 =0.9,an d F(x 2 )=1.4whiley 2 =1.3...Howcan youimprovet hismodel ?

Ruleofthegame:

Youaren otallowedt oremov eanythingfromForchan geany parameterinF.

GradientBoostingforRegr ession

Let'splayagame.. .

Youaregi ven(x

1 ,y 1 ),(x 2 ,y 2 ),...,(x n ,y n ),andt het askistofi ta modelF(x)to minimi zesquareloss. Supposeyourfriendwa ntstohelp youandgivesyouamodel F. Youchec khismodelandfin dthemodel isgoodbutnotperf ect.

Therearesomemist akes:F(x

1 )=0.8,wh iley 1 =0.9,an d F(x 2 )=1.4whiley 2 =1.3...Howcan youimprovet hismodel ?

Ruleofthegame:

Youaren otallowedt oremov eanythingfromForchan geany parameterinF. Youcana ddanaddit ionalmode l(regre ssiontree)htoF,so thenewpre dictionwil lbeF(x)+h(x).

GradientBoostingforRegr ession

Simplesolution:

Youwish toimprovethem odels uchthat

F(x 1 )+h(x 1 )=y 1 F(x 2 )+h(x 2 )=y 2 F(x n )+h(x n )=y n

GradientBoostingforRegr ession

Simplesolution:

Or,equiva lently,youwish

h(x 1 )=y 1 !F(x 1 h(x 2 )=y 2 !F(x 2 h(x n )=y n !F(x n

GradientBoostingforRegr ession

Simplesolution:

Or,equiva lently,youwish

h(x 1 )=y 1 !F(x 1 h(x 2 )=y 2 !F(x 2 h(x n )=y n !F(x n

Cananyregr essiontree hachievethisgoalperfectl y?

GradientBoostingforRegr ession

Simplesolution:

Or,equiva lently,youwish

h(x 1 )=y 1 !F(x 1 h(x 2 )=y 2 !F(x 2 h(x n )=y n !F(x n

Cananyregr essiontree hachievethisgoalperfectl y?

Maybenot....

GradientBoostingforRegr ession

Simplesolution:

Or,equiva lently,youwish

h(x 1 )=y 1 !F(x 1 h(x 2 )=y 2quotesdbs_dbs17.pdfusesText_23