斯坦福机器学习讲义(全)Stanford Machine Leaning.pdf

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1、CS229LecturenotesAndrewNgSupervisedlearningLetsstartbytalkingaboutafewexamplesofsupervisedlearningproblems.Supposewehaveadatasetgivingthelivingareasandpricesof47housesfromPortland,Oregon:Livingarea(feet2)Price(1000$s)21044001600330240036914162323000540......Wecanplot

2、thisdata:housingprices1000900800700600500price(in$1000)4003002001000500100015002000250030003500400045005000squarefeetGivendatalikethis,howcanwelearntopredictthepricesofotherhousesinPortland,asafunctionofthesizeoftheirlivingareas?1CS229Winter20032Toestablishnotationfo

3、rfutureuse,we’llusex(i)todenotethe“input”variables(livingareainthisexample),alsocalledinputfeatures,andy(i)todenotethe“output”ortargetvariablethatwearetryingtopredict(price).Apair(x(i),y(i))iscalledatrainingexample,andthedatasetthatwe’llbeusingtolearn—alistofmtrainin

4、gexamples{(x(i),y(i));i=1,...,m}—iscalledatrainingset.Notethatthesuperscript“(i)”inthenotationissimplyanindexintothetrainingset,andhasnothingtodowithexponentiation.WewillalsouseXdenotethespaceofinputvalues,andYthespaceofoutputvalues.Inthisexample,X=Y=R.Todescribethes

5、upervisedlearningproblemslightlymoreformally,ourgoalis,givenatrainingset,tolearnafunctionh:X7→Ysothath(x)isa“good”predictorforthecorrespondingvalueofy.Forhistoricalreasons,thisfunctionhiscalledahypothesis.Seenpictorially,theprocessisthereforelikethis:TrainingsetLearn

6、ingalgorithmxhpredictedy(livingareaof(predictedprice)house.)ofhouse)Whenthetargetvariablethatwe’retryingtopredictiscontinuous,suchasinourhousingexample,wecallthelearningproblemaregressionprob-lem.Whenycantakeononlyasmallnumberofdiscretevalues(suchasif,giventhelivinga

7、rea,wewantedtopredictifadwellingisahouseoranapartment,say),wecallitaclassificationproblem.3PartILinearRegressionTomakeourhousingexamplemoreinteresting,letsconsideraslightlyricherdatasetinwhichwealsoknowthenumberofbedroomsineachhouse:Livingarea(feet2)#bedroomsPrice(100

8、0$s)2104340016003330240033691416223230004540.........Here,thex’saretwo-dimensionalvectorsinR2.Forinstance,x(i)isthe1(i)livingareaof