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1、AnIntroductiontoRestrictedBoltzmannMachinesAsjaFischer1,2andChristianIgel21Institutf¨urNeuroinformatik,Ruhr-Universit¨atBochum,Germany2DepartmentofComputerScience,UniversityofCopenhagen,DenmarkAbstract.RestrictedBoltzmannmachines(RBMs)areprobabilisticgraphicalmodelsthatcanbeinterpretedassto
2、chasticneuralnetworks.Theincreaseincomputationalpowerandthedevelopmentoffasterlearn-ingalgorithmshavemadethemapplicabletorelevantmachinelearningproblems.Theyattractedmuchattentionrecentlyafterbeingproposedasbuildingblocksofmulti-layerlearningsystemscalleddeepbeliefnet-works.Thistutorialintr
3、oducesRBMsasundirectedgraphicalmodels.Thebasicconceptsofgraphicalmodelsareintroducedfirst,however,basicknowledgeinstatisticsispresumed.DifferentlearningalgorithmsforRBMsarediscussed.AsmostofthemarebasedonMarkovchainMonteCarlo(MCMC)methods,anintroductiontoMarkovchainsandtherequiredMCMCtechniqu
4、esisprovided.1IntroductionBoltzmannmachines(BMs)havebeenintroducedasbidirectionallyconnectednetworksofstochasticprocessingunits,whichcanbeinterpretedasneuralnet-workmodels[1,16].ABMcanbeusedtolearnimportantaspectsofanunknownprobabilitydistributionbasedonsamplesfromthisdistribution.Ingeneral
5、,thislearningprocessisdifficultandtime-consuming.However,thelearningproblemcanbesimplifiedbyimposingrestrictionsonthenetworktopology,whichleadsustorestrictedBoltzmannmachines(RBMs,[34]),thetopicofthistutorial.A(restricted)BMisaparameterizedgenerativemodelrepresentingaprob-abilitydistribution.G
6、ivensomeobservations,thetrainingdata,learningaBMmeansadjustingtheBMparameterssuchthattheprobabilitydistributionrepre-sentedbytheBMfitsthetrainingdataaswellaspossible.Boltzmannmachinesconsistoftwotypesofunits,socalledvisibleandhiddenneurons,whichcanbethoughtofasbeingarrangedintwolayers.Thevis
7、ibleunitsconstitutethefirstlayerandcorrespondtothecomponentsofanobservation(e.g.,onevisibleunitforeachpixelofadigitalinputimage).Thehiddenunitsmodeldependenciesbetweenthecomponentsofobservations(e.g.,dependenciesbetweenpixelsinimages).Theycanbeviewedasnon
