I. Decision trees II. Ensamble methods: Mixtures of experts
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1 CS 75 Machne Learnn Lectre 4 I. Decson trees II. Ensamble methods: Mtres of eperts Mlos Hasrecht mlos@cs.ptt.ed 539 Sennott Sqare CS 75 Machne Learnn Eam: Aprl 8 7 Schedle Term proects & proect presentatons: Aprl 5 7 At :-4:pm n SNSQ 533 No class: on Aprl 3 7 CS 75 Machne Learnn
2 Decson trees An alternatve approach to classfcaton: Partton the npt space to reons Classf ndependentl n ever reon CS 75 Machne Learnn Decson trees The parttonn dea s sed n the decson tree model: Splt the space recrsvel accordn to npts n Classf assn class label at the bottom of the tree Eample: Bnar classfcaton {} Bnar attrbtes 3 3 t f t f t f CS 75 Machne Learnn
3 Decson trees How to constrct the decson tree? Top-bottom alorthm: Fnd the best splt condton qantfed based on the mprt measre on the trann set Stops when no mprovement possble Imprt measre: Measres how well are the two classes separated Ideall we wold le to separate all s and Splts of fnte vs. contnos vale attrbtes Contnos vale attrbtes condtons: 3. 5 CS 75 Machne Learnn Let Imprt measre D - Total nmber of data entres D - Nmber of data entres classfed as D p - rato of nstances classfed as D Imprt measre defnes how well are the classes n the trann dataset separated In eneral the mprt measre shold satsf: Larest when data are splt evenl to classes p nmber of classes Shold be when all data belon to the same class CS 75 Machne Learnn
4 Imprt measres There are varos mprt measres sed n the lteratre Entrop based measre Qnlan C4.5 I D Entrop D p lo p Eample for Gn measre Breman CART I D Gn D CS 75 Machne Learnn p Decson-tree bldn Gan de to splt epected redcton n the mprt measre entrop eample Gan D A Entrop v D t EntropD D v Vales A CS 75 Machne Learnn v D Entrop D D - a partton of D wth the vale of attrbte A v 3 f EntropD t t f t f Entrop D Entrop D v 3 f
5 Decson tree learnn Greed learnn alorthm: Repeat ntl no or small mprovement n the prt Fnd the attrbte wth the hhest an Add the attrbte to the tree and splt the set accordnl Blds the tree n the top-down fashon Gradall epands the leaves of the partall blt tree The method s reed It loos at a snle attrbte and an n each step Ma fal when the combnaton of attrbtes s needed to mprove the prt part fnctons CS 75 Machne Learnn Decson tree learnn Lmtatons of reed methods Cases n whch a combnaton of two or more attrbtes mproves the mprt CS 75 Machne Learnn
6 Decson tree learnn B redcn the mprt measre we can row ver lare trees Problem: Overfttn We ma splt and classf ver well the trann set bt we ma do worse n terms of the eneralzaton error Soltons to the overfttn problem: Solton. Prne branches of the tree blt n the frst phase Use nternal valdaton set to test for the overft Solton. Test for the overft n the tree bldn phase Stop bldn the tree when performance on the valdaton set deterorates CS 75 Machne Learnn Mtre of eperts model Ensamble methods: Use a combnaton of smpler learners to mprove predctons Mtre of epert model: Dfferent npt reons covered wth dfferent learners A soft swtchn between learners Mtre of eperts Epert learner CS 75 Machne Learnn
7 Mtre of eperts model Gatn networ : decdes what epert to se... - atn fnctons Gatn networ Epert Epert... Epert CS 75 Machne Learnn Learnn mtre of eperts Learnn conssts of two tass: Learn the parameters of ndvdal epert networs Learn the parameters of the atn networ Decdes where to mae a splt Assme: atn fnctons ve probabltes... Based on the probablt we partton the space parttons belons to dfferent eperts How to model the atn networ? A mltwa classfer model: softma model a eneratve classfer model CS 75 Machne Learnn
8 CS 75 Machne Learnn Learnn mtre of eperts Assme we have a set of lnear eperts Assme a softma atn networ Lelhood of assmed that errors for dfferent eperts are normall dstrbted wth the same varance T µ ep ep T T p Note: bas terms are hdden n Θ p P P Θ ep ep ep σ µ σ π T T CS 75 Machne Learnn Learnn mtre of eperts Gradent learnn. On-lne pdate rle for parameters of epert If we now the epert that s responsble for If we do not now the epert µ α + h µ α + h - responsblt of the th epert a nd of posteror p p h / ep / ep µ µ -a pror ep... - a lelhood
9 Learnn mtres of eperts Gradent methods On-lne learnn of atn networ parameters + β h The learnn wth condtoned mtres can be etended to learnn of parameters of an arbtrar epert networ e.. lostc reresson mltlaer neral networ l + β l µ µ l h µ CS 75 Machne Learnn Learnn mtre of eperts EM alorthm offers an alternatve wa to learn the mtre Alorthm: Intalze parameters Θ Repeat Set Θ ' Θ. Epectaton step Q Θ Θ' EH X YΘ' lo P H Y X Θ ξ. Mamzaton step Θ ar ma Q Θ Θ ' Θ ntl no or small mprovement n Q Θ Θ' Hdden varables are denttes of epert networs responsble for data ponts CS 75 Machne Learnn
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