Human Unsupervised and Supervised Learning as A Quantitative Distinction

cWorldScientificPublishingCompany󰀁

HUMANUNSUPERVISEDANDSUPERVISEDLEARNING

ASAQUANTITATIVEDISTINCTION

TODDM.GURECKIS∗andBRADLEYC.LOVE†DepartmentofPsychology,UniversityofTexasatAustin,1UniversityStationA8000,Austin,TX78712-0187,USA

∗gureckis@love.psy.utexas.edu†love@love.psy.utexas.eduhttp://love.psy.utexas.edu/

SUSTAIN(SupervisedandUnsupervisedSTratifiedAdaptiveIncrementalNetwork)isanetworkmodelofhumancategorylearning.SUSTAINinitiallyassumesasimplecategorystructure.IfsimplesolutionsproveinadequateandSUSTAINisconfrontedwithasurprisingevent(e.g.itistoldthatabatisamammalinsteadofabird),SUSTAINrecruitsanadditionalclustertorepresentthesurprisingevent.Newlyrecruitedclustersareavailabletoexplainfutureeventsandcanthemselvesevolveintoprototypes/attractors/rules.SUSTAINhasexpandedthescopeoffindingsthatmodelsofhumancategorylearningcanaddress.ThispaperextendsSUSTAINtoaccountforbothsupervisedandunsupervisedlearningdatathroughacommonmechanism.Themodifiedmodel,uSUSTAIN(unifiedSUSTAIN),issuccessfullyappliedtohumanlearningdatathatcomparesunsupervisedandsupervisedlearningperformances.18Keywords:Category;learning;unsupervised;supervised;psychology.

1.Introduction

Categoriesprovideacrucialfunctionunderlyingthecognitiveabilitiesofhumans.Theyallowustogeneralizeourknowledgetonovelsituationsandtoinferunknownpropertiesoftheenvironment.Theseabilitiesareindispensabletoanyintelligentsystem.

Researchersstudyinghumancategorizationhavetraditionallyfocusedonhumanperformanceinsupervisedlearningtasks(seeRefs.2,4and7forsomeexceptions).Inthisexperimentalparadigm,subjectslearntoclassifystimuliasmembersofcontrastivecategoriesthroughtrialbytriallearningwithcorrectivefeedback.Theories(andmodels)oflearningarefavoredthatcanaccountfortherelativedifficultyofacquiringdifferentcategorystructures.25,30

Althoughclassificationlearningdoescaptureaspectsofhumanlearning,othersarenotaddressedbythisparadigm.Forinstance,humanscanspontaneouslyconstructcategoriesintheabsenceoffeedback.Asanexample,manyofushavecreatedthecategories“interesting”emailand“junk”emailintheabsenceof

885

886T.M.Gureckis&B.C.Love

explicitfeedback.Suchlearningisreferredtoasunsupervisedlearning.Supervisedandunsupervisedlearningareoftenseenasbeingqualitativelydifferent.Super-visedlearningischaracterizedasintentional,inthatlearnersactivelysearchforrules(perhapsbyhypothesistesting)andareexplicitlyawareoftheruletheyareconsidering.26Ontheotherhand,unsupervisedlearningisseenasanincidental,undirected,stimulusdriven,andincrementalaccrualofinformation.3,8,13,14,17

Incontrasttothisview,Love18hasfoundthatintentionalunsupervisedlearningperformanceismoresimilartosupervisedlearningperformancethanitistoincidentalunsupervisedlearningperformance.Thisresultsuggeststhattheunsupervised/superviseddichotomymaynotbevalid.GureckisandLove10havearguedthatunsupervisedandsupervisedlearningcanbemodeledthroughacom-monmechanism.However,ouraccounthasyettomodeltoadirectcompari-sonbetweensupervisedandunsupervisedlearning.Here,weapplyGureckisandLove’s10variantoftheSUSTAIN(SupervisedandUnsupervisedSTratifiedAdap-tiveIncrementalNetwork)model,referredtoasuSUSTAIN(unifiedSUSTAIN),totheLove18datauSUSTAINdiffersfromothermodelsthatseektounifyun-supervisedandsupervisedlearning,suchasAnderson’s1rationalmodel,inthatuSUSTAINisapplicabletobothunsupervisedandsupervisedlearningtaskswhilenotpredictingthatthesetasksleadtoequivalentperformance(whichtheydonot).Intheremainderofthispaper,weoverviewSUSTAINanduSUSTAIN.WethenfituSUSTAINtotheLove18dataandconsidertheimplicationsofthesimulations.2.TheModelingApproach:SUSTAINanduSUSTAIN

SUSTAINhasbeensuccessfullyappliedtoanarrayofchallenginghumandatasetsspanningavarietyofcategorylearningparadigmsincludingclassificationlearning,21learningatdifferentlevelsofabstraction,20inferencelearning,19andunsupervisedlearning.11,22

Inthefollowingsections,wediscussSUSTAIN’soperation,itsunderlyingprinciples,andthemathematicalequationsthatfollowfromtheseprinciples.WethenintroduceamodificationtoSUSTAINthatenablesittoaccountforsupervisedandunsupervisedlearningdatathroughasinglerecruitmentmechanism.Thismechanismmakesuseofanintuitiveandgeneralnotionofsurprisetofacilitatelearning.ThismodifiedversionofSUSTAINisreferredtoasuSUSTAIN.2.1.Overviewofmodel

SUSTAINisanetworkmodelofhumancategorylearning.Oneachlearningtrial,SUSTAINtakesasinputadescriptionofthecurrentstimulusitemrepresentedtothemodelbyasetofperceptualfeaturedimensions.Forexample,astimulusitemdepictingalarge,purplesquarewillberepresentedtothemodelbythefea-turedimensionscolor,sizeandstripe.Likeothermodelsofcategorylearning(suchasRef.1),SUSTAINtreatsthecategorymembership(orcategorylabel)ofasti-mulusitemasanotherstimulusfeaturedimension.SUSTAINmaintainsaselective

HumanUnsupervisedandSupervisedLearningasaQuantitativeDistinction887

attentionmechanismwhichallowsittolearntofocusattentiononstimulusdimensionsthatareparticularlyusefulforthecurrentcategorizationtask(similartoRef.16).

Theinternalrepresentationsinthemodelconsistofasetofclusters.Categoriesarerepresentedinthemodelasoneormoreassociatedclusters.Initially,thenetworkhasonlyoneclusterthatiscentereduponthefirstinputpattern.Asnewstimulusitemsarepresented,themodelattemptstoassignthesenewitemstoanexistingcluster.Thisassignmentisdonethroughanunsupervisedprocedurebasedonthesimilarityofthenewitemtothestoredclusters.Whenanewitemisassignedtoacluster,theclusterupdatesitsinternalrepresentationtobecometheaverageofallitemsassignedtotheclustersofar.

However,ifSUSTAINdiscoversthroughfeedbackthatthissimilarity-basedassignmentisincorrect,anewclusteriscreatedtoencodethecurrentitemasanexception(foraconcreteexampleofthisseePrinciple3inthefollowingsection).Inunsupervisedlearningtasksthereisnocorrectivefeedback,soinsteadSUSTAINcreatesanewclusterifthecurrentstimulusitemisnotsufficientlysimilartoanyexistingclusters(thethresholdforthissufficiencyiscontrolledbyaparameterinthemodel).Bothoftheseclusterrecruitmentstrategiesareunifiedundertheprincipeof“adaptationtosurprise”.10Insupervisedlearning,SUSTAINcreatesanewclusterinresponsetoasurprisingmisclassification,whereasinunsupervisedlearning,anewclusteriscreatedwhenthemodelencountersasurprisinglynovelstimulusitem.

Clusterscompetewitheachothertorespondtothecurrentstimulusitem.Theclusterthatwinsthiscompetitionpassesitsactivationoverconnectionweightstoasetofoutputunits.Theseoutputunitsreplicatethestructureoftheinputdimensions.Theconnectionweightsareadjustedoverthecourseoflearningsothattheassociationbetweeneachclusterandtheappropriateresponseformembersofthatclusterisstrengthened.Forexample,aclusterwhosemembersaremostlyincategory“A”woulddevelopoverthecourseoflearningastrongerconnectiontothecategory“A”outputunitthantothecategory“B”outputunit.Theactivationofanoutputunitisproportionaltothestrengthoftheactivationpassedfromthewinningclusterandthestrengthoftheconnectionweight.SUSTAIN’sultimateresponseisbiasedtowardsthemostactivatedoutputunit.Inthisway,classificationdecisionsareultimatelybasedontheclustertowhichaninstanceisassigned.2.2.ThekeyprinciplesofSUSTAIN

Withthisgeneralunderstandingoftheoperationofthemodelinmind,wenowexaminethefivekeyprinciplesofSUSTAIN.Theseprincipleshighlighttheimpor-tantfeaturesofthemodelandprovidethefoundationforthemodel’sformalism.2.2.1.Principle1,SUSTAINisbiasedtowardssimplesolutions

SUSTAINisinitiallydirectedtowardssimplesolutions.Atthestartoflearning,SUSTAINhasonlyoneclusterwhichiscenteredonthefirstinputitem.Itthen

888T.M.Gureckis&B.C.Love

addsclusters(i.e.complexity)onlyasneededtoaccuratelydescribethecategorystructure.Likeothermodelsofcategorylearning(e.g.Ref.16),SUSTAINlearnstoselectivelyattendtostimulusfeaturedimensionsthataremostusefulforcategorization.ThisfocusonasubsetofstimulusdimensionsalsoservestobiasSUSTAINtowardssimplesolutions.

2.2.2.Principle2,similarstimulusitemstendtoclustertogether

Inlearningtoclassifystimuliasmembersoftwodistinctcategories,SUSTAINwillclustersimilaritemstogether.Forexample,differentinstancesofabirdsubtype(e.g.sparrows)couldclustertogetherandformasparrowclusterinsteadofleavingseparatetracesinmemoryforeachinstance.Clusteringisanunsupervisedprocessbecauseclusterassignmentisdoneonthebasisofsimilarity,notfeedback.2.2.3.Principle3,SUSTAINlearnsinbothasupervisedand

unsupervisedfashion

Inlearningtoclassifythecategories“birds”and“mammals”,SUSTAINreliesonbothunsupervisedandsupervisedlearningprocesses.ConsideralearningtrialinwhichSUSTAINhasformedaclusterwhosemembersaresmallbirds,andanotherclusterwhosemembersarefour-leggedmammals.IfSUSTAINissubsequentlyaskedtoclassifyabat,itwillinitiallypredictthatabatisabirdonthebasisofoverallsimilarity(batsandbirdsarebothsmall,havewings,fly,etc.).Uponreceivingfeedbackfromtheenvironment(supervision)indicatingthatabatisamammal,SUSTAINwillrecruitanewclustertorepresentthebatasanexceptiontothemammalcategory.ThenexttimeSUSTAINisexposedtothebatoranothersimilarbat,SUSTAINwillcorrectlypredictthatabatisamammal.ThisexamplealsoillustrateshowSUSTAINcanentertainmorecomplexsolutionswhennecessarythroughclusterrecruitment(seePrinciple1).2.2.4.Principle4,thepatternoffeedbackmatters

Astheexampleusedaboveillustrates,feedbackaffectstheinferredcategorystructure.Predictionfailuresresultinaclusterbeingrecruited,thusdifferentpatternsoffeedbackcanleadtodifferentrepresentationsbeingacquired.ThisprincipleallowsSUSTAINtopredictdifferentacquisitionpatternsfordifferentlearningmodesthatareinformationallyequivalentbutdifferintheirpatternoffeedback.ThelearningconditionsintheLove18studyconsideredinthispaperareinformationallyequivalent,butdifferintheirpatternoffeedback.2.2.5.Principle5,clustercompetition

Clusterscanbeseenascompetingexplanationsoftheinput.Thestrengthoftheresponsefromthewinningcluster(theclusterthecurrentstimulusismostsimilar

HumanUnsupervisedandSupervisedLearningasaQuantitativeDistinction8

to)isattenuatedinthepresenceofotherclustersthataresomewhatsimilartothecurrentstimulus(seeRef.31,accountofcompetingexplanationsinreasoning).2.3.MathematicalformulationofSUSTAIN

ThissectionofthepaperexplainshowthegeneralprinciplesthatgovernSUSTAIN’soperationareimplementedinanalgorithmicmodel.2.3.1.Inputrepresentation

Stimuliarerepresentedinthemodelasvectorframeswherethedimensionalityofthevectorisequaltothedimensionalityofthestimuli.Thecategorylabelisalsoincludedasastimulusdimension.Thus,stimulithatvaryonthreeper-ceptualdimensions(e.g.size,shapeandcolor)andaremembersofoneoftwocategorieswouldrequireavectorframewithfourdimensions.Afour-dimensionalbinary-valuedstimulus(threeperceptualdimensionsplusthecategorylabel)canbethoughtofasafourcharacterstring(e.g.1211)inwhicheachcharacterrepresentsthevalueofastimulusdimension.Forexample,thefirstcharactercoulddenotethesizedimensionwitha1indicatingasmallstimulusanda2indicatingalargestimulus.

Ofcourse,alearningtrialusuallyinvolvesanincompletestimulusrepresenta-tion.Forinstance,inclassificationlearningalltheperceptualdimensionsareknown,butthecategorylabeldimensionisunknownandqueried.Afterthelearnerre-spondstothequery,correctivefeedbackisprovided.Assumingthefourthstimulusdimensionisthecategorylabeldimension,theclassificationtrialfortheabovestimulusisrepresentedas121?→1211.

Oneveryclassificationtrial,thecategorylabeldimensionisqueriedandcorrectivefeedbackindicatingthecategorymembershipofthestimulusisprovided.Incontrast,oninferencelearningtrials,subjectsaregiventhecategorymember-shipoftheitem,butmustinferanunknownstimulusdimension.Possibleinferencelearningtrialsfortheabovestimulusdescriptionare?211→1211,1?11→1211,and12?1→1211.Noticethatinferenceandclassificationlearningprovidethelearnerwiththesamestimulusinformationafterfeedback(thoughthepatternoffeedbackvaries).

Unsupervisedlearningdoesnotinvolveinformativefeedback.Inunsupervisedlearning,everyitemisconsideredtobeamemberofthesameglobalcategory.Thus,thecategorylabeldimensionisunitaryvaluedanduninformativefordifferentiatingbetweenstimuli.However,thedegreetowhichanyparticularstimulusactivatesthiscategorydimensionindicatesthedegreetowhichthenetworkrecognizesthestimulus.

Inordertorepresentanominalstimulusdimensionthatcandisplaymultiplevalues,SUSTAINdevotesmultipleinputunits.Torepresentanominaldimensioncontainingkdistinctvalues,kinputunitsareutilized.Alltheunitsformingadimensionaresettozero,exceptfortheoneunitthatdenotesthenominalvalue

0T.M.Gureckis&B.C.Love

ofthedimension(thisunitissettoone).Forexample,thestimulusdimensionofmaritalstatushasthreevalues(“single”,“married”,“divorced”).Thepattern[010]representsthedimensionvalueof“married”.AcompletestimulusisrepresentedbythevectorIposikwhereiindexesthestimulusdimensionandkindexesthenominalvaluesfordimensioni.Forexample,ifmaritalstatuswasthethirdsti-mulusdimensionandthesecondvaluewaspresent(i.e.married),thenIpos32wouldequalone,whereasIpos31andIpos33wouldequalzero.The“pos”inIposdenotesthatthecurrentstimulusislocatedataparticularpositioninamultidimensionalrepresentationalspace.2.3.2.Receptivefields

Eachclusterhasareceptivefieldforeachstimulusdimension.Acluster’sreceptivefieldforagivendimensioniscenteredatthecluster’spositionalongthatdimension.Thepositionofaclusterwithinadimensionindicatesthecluster’sexpectationsforitsmembers.

Thetuningofareceptivefield(asopposedtothepositionofareceptivefield)determineshowmuchattentionisbeingdevotedtothestimulusdimension.Allthereceptivefieldsforastimulusdimensionhavethesametuning(i.e.atten-tionisdimension-wideasopposedtocluster-specific).Areceptivefield’stuningchangesasaresultoflearning.ThischangeinreceptivefieldtuningimplementsSUSTAIN’sselectiveattentionmechanism.Dimensionsarehighlyattendedtodeveloppeakedtunings,whereasdimensionsarenotwellattendedtodevelopbroadtunings.Dimensionsthatprovideconsistentinformationattheclusterlevelreceivegreaterattention.

Mathematically,receptivefieldshaveanexponentialshapewithareceptivefield’sresponsedecreasingexponentiallyasdistancefromitscenterincreases.Theactivationfunctionforadimensionis:

α(µ)=λe−λµ

(1)

whereλisthetuningofthereceptivefield,µisthedistanceofthestimulusfromthecenterofthefield,andα(µ)denotestheresponseofthereceptivefieldtoastimulusfallingµunitsfromthecenterofthefield.ThechoiceofexponentiallyshapedreceptivefieldsismotivatedbyShepard’s29workonstimulusgeneralization.

Althoughreceptivefieldswithdifferentλhavedifferentshapes(rangingfromabroadtoapeakedexponential),foranyλ,thearea“underneath”areceptivefieldisconstant:

󰀄∞󰀄∞

α(µ)dµ=λe−λµdµ=1.(2)

0

0

Foragivenµ,λthatmaximizesα(µ)canbecomputedfromthederivative:

∂α

HumanUnsupervisedandSupervisedLearningasaQuantitativeDistinction1

2.3.3.Clusteractivation

Withnominalstimulusdimensions,thedistanceµij(from0to1)betweentheithdimensionofthestimulusandclusterj’spositionalongtheithdimensionis:

µij=

1

act

whereHjistheactivationofthejthcluster,misthenumberofstimulusdimensions,λiisthetuningofthereceptivefieldfortheithinputdimension,andrisanattentionalparameter(alwaysnon-negative).Whenrislarge,inputunitswithtightertunings(unitsthatseemrelevant)dominatetheactivationfunction.Dimensionsthatarehighlyattendedhavelargerλsandwillhavegreaterimportanceindeterminingtheclusters’activationvalues.Increasingrsimplyaccentuatesthiseffect.Ifrissettozero,everydimensionreceivesequalattention.Equation(5)sumsuptheresponsesofthereceptivefieldsforeachinputdimensionandnormalizesthesum(again,highlyattendeddimensionsweighheavily).Clusteractivationisboundbetween0(exclusive)and1(inclusive).Unknownstimulusdimensions(e.g.thecategorylabelinaclassificationtrial)arenotincludedintheabovecalculation.

󰀂m

r

i=1(λi)

(5)

2.3.4.Competition

Clusterscompetetorespondtoinputpatternsandinturninhibitoneanother.

out

Whenmanyclustersarestronglyactivated,theoutputofthewinningclusterHjisless:

ForthewinningHjwiththegreatestH

act

,

outHj

=

actβ(Hj)

2T.M.Gureckis&B.C.Love

Clustersotherthanthewinnerhavetheiroutputsettozero.Equation(6)isastraightforwardmethodforimplementinglateralinhibition.Itisahighleveldescriptionofaniterativeprocesswhereunitssendsignalstoeachotheracrossinhibitoryconnections.Psychologically,Eq.(6)signifiesthatcompetingalternativeswillreduceconfidenceinachoice(reflectedinaloweroutputvalue).2.3.5.Response

Activationisspreadfromtheclusterstotheoutputunitsofthequeried(theunknown)stimulusdimensionz:

outCzk

=

n󰀃j=1

out

wj,zkHj

(7)

out

whereCzkistheoutputoftheoutputunitrepresentingthekthnominalvalueofthequeried(unknown)zthdimension,nisthenumberofclusters,andwj,zkistheweightfromclusterjtocategoryunitCzk.Awinningcluster(especiallyonethatdidnothavemanycompetitorsandissimilartothecurrentinputpattern)thathasalargepositiveconnectiontoanoutputunitwillstronglyactivatetheoutputunit.Thesummationintheabovecalculationisnotreallynecessarygiventhatonlythewinningclusterhasanonzerooutput,butisincludedtomakethesimilaritiesbetweenSUSTAINandothermodelsmoreapparent.

Theprobabilityofmakingresponsek(thekthnominalvalue)forthequerieddimensionzis

Pr(k)=

e(d·Czk

out

)

HumanUnsupervisedandSupervisedLearningasaQuantitativeDistinction3

Anewclusterisrecruitedifthewinningclusterpredictsanincorrectresponse.Inthecaseofasupervisedlearningsituation,aclusterisrecruitedaccordingtothefollowingprocedure:

Forthequerieddimensionz,iftzkdoesnotequal1fortheCzk

out

withthelargestoutputCzkofallCz∗,thenrecruitanewcluster.

(10)

Inotherwords,theoutputunitrepresentingthecorrectnominalvaluemustbethemostactivatedofalltheoutputunitsformingthequeriedstimulusdimension.Inthecaseofanunsupervisedlearningsituation,SUSTAINisself-supervisingandrecruitsaclusterwhenthemostactivatedclusterHj’sactivationisbelowthethresholdτ:

act

if(Hj<τ),thenrecruitanewcluster.

(11)

UnsupervisedrecruitmentinSUSTAINbearsastrongresemblancetorecruitment

inAdaptiveResonanceTheory,5ClapperandBower’squalitativemodel,6andHartigan’sleaderalgorithm.12

Whenanewclusterisrecruiteditiscenteredonthemisclassifiedinputpatternandtheclusters’activationsandoutputsarerecalculated.Thenewclusterthenbecomesthewinnerbecauseitwillbethemosthighlyactivatedcluster(itiscentereduponthecurrentinputpattern—allµijwillbezero).Again,SUSTAINbeginswithaclustercenteredonthefirststimulusitem.Thepositionofthewinnerisadjusted:

ForthewinningHj,∆Hj

posik

=η(Iposik−Hj

posik

)(12)

whereηisthelearningrate.Thecentersofthewinner’sreceptivefieldsmovetowardstheinputpatternaccordingtotheKohonenlearningrule.15Thislearningrulecenterstheclusteramidstitsmembers.

UsingourresultfromEq.(3),receptivefieldtuningsareupdatedaccordingto:

∆λi=ηe−λiµij(1−λiµij)

(13)

wherejistheindexofthewinningcluster.

Onlythewinningclusterupdatesthevalueofλi.Equation(13)adjuststhepeakednessofthereceptivefieldforeachinputsothateachinputdimensioncanmaximizeitsinfluenceontheclusters.Initially,λiissettobebroadlytunedwithavalueof1.Thevalueof1ischosenbecausethemaximaldistanceµijis1andtheoptimalsettingofλiforthiscaseis1(i.e.Eq.(13)equalszero).Underthisscheme,λicannotbecomelessthan1,butcanbecomemorenarrowlytuned.

Whenaclusterisrecruited,weightsfromtheunittotheoutputunitsaresettozero.Theonelayerdeltalearningrule32,28isusedtoadjusttheseweights:

outout

∆wj,zk=η(tzk−Czk)Hj,

(14)

wherezisthequerieddimension.Notethatonlythewinningclusterwillhaveits

weightsadjustedsinceitistheonlyclusterwithanonzerooutput.

4T.M.Gureckis&B.C.Love

2.4.uSUSTAIN:aunifiedapproachtosupervisedand

unsupervisedlearning

SUSTAINcanmodelbothsupervisedandunsupervisedlearning,butitreliesondifferentrecruitmentmechanisms.Inbothcases,aclusterisrecruitedinresponsetoasurprisingevent(i.e.theexistingclusterstructuredoesnotproperlycharacterizethecurrentstimulus),buthowasurprisingeventisdefineddiffers.Inthesupervisedcase,thesurprisingeventisapredictionerror,whereasinthecaseofunsupervisedlearningthesurprisingeventisanunfamiliarstimulus.

Althoughthetwoseparaterecruitmentprocedureshavebeensuccessful,asinglerecruitmentprocedureispreferable.Beyondparsimony,aunifiedaccountcouldproveusefulinclarifyingtherelationshipbetweenunsupervisedandsupervisedlearning.Asimplewaytointegratethetworecruitmentstrategiesistogeneralizetheunsupervisedproceduresothatitisapplicabletosupervisedlearningsituations.Underthisscheme,anewclusterisrecruitedwhenthecurrentstimulusisnotsufficientlysimilartoanyclusterinitscategory:

Forthequerieddimensionz,

act

IfMax({Hj|µzj=0})<τ,thenrecruitanewcluster,

(15)

act

istheactivationofclusterj,µzjisthedistance[asdefinedinEq.(4)]whereHj

alongthezthdimensionofthecurrentstimulusandclusterj’spositionalongthezthdimension,andτisaconstantbetween0and1(aparameter).Therequirementthatµzjbezerospecifiesthatonlyclustersassociatedwiththecategoryofthecurrentstimulusareconsidered.Inunsupervisedlearning,allitemsbelongtothesameglobalcategorywhichrepresentsitemsthenetworkhasseenbefore.Thus,

act

|µzj=0})referstothemostactivatedclusteroverall.InsupervisedMax({Hj

learning,themostactivatedclusterpredictingthecorrectcategorymaynotbethemostactivatedclusteroverall.

Besidesprovidingaunifiedframework,thisrecruitmentstrategyhasanumberofothervirtuesoverSUSTAIN’soriginalrecruitmentrule[Eq.(10)]forsupervisedlearning.Forexample,theunifiedprocedurewillrecruitanewclusterwhenanunusualitemisencounteredthatdoesnotresultinapredictionerrorwhereasthepreviouserror-drivenrecruitmentschemewouldnotrecruitanewclustertoencodetheunusualitem.Assigningaveryunusualitemtoanexistingcluster(aclustertheitemisnotverysimilarto)couldresultincatastrophicinterference(seeRef.27)astheclustermustundergoradicalchangetoaccommodateitsnewestmember.

3.EvaluatinguSUSTAIN

InordertoevaluatethisunifiedformulationofthemodelweapplieduSUSTAINtothestudiespreviouslyaccountedforusingseparateclusterrecruitmentmech-anismsforsupervisedandunsupervisedlearning.10ItisimportanttorecognizethattherecruitmentprocedurethatuSUSTAINusesis,infact,ageneralizationofunsupervisedrecruitmentprocedureusedbytheoriginalSUSTAINmodel.Thus,

HumanUnsupervisedandSupervisedLearningasaQuantitativeDistinction5

uSUSTAINandSUSTAINprovideequivalentaccountsofunsupervisedlearning.9uSUSTAINandSUSTAINhavefitanumberofunsupervisedlearningstudiesandhavegeneratednovelpredictionsthathavebeensubsequentlytestedandconfirmedwithhumansubjects.11

AtruetestofgeneralityoftheuSUSTAINapproachliesinitsabilitytofitsupervisedlearningdata.GureckisandLove9applieduSUSTAINtoanumberofsupervisedlearningstudiesandfoundthatuSUSTAINapproximatedSUSTAIN’ssuccesses.Despiteitssimplicity,theunifiedrecruitmentprocedureinuSUSTAINhasprovenremarkablysuccessfulinthisdomain.

AlthoughuSUSTAINhasdemonstratedtheabilitytoaccountforhumanlearningperformanceacrossawiderangeofcategorylearningparadigms,ithasneverbeenappliedtoastudyspecificallydesignedtocompareunsupervisedandsupervisedlearning.Giventhepastsuccessesofthemodel,itwouldbeinformativetoapplythemodeltoadirectcomparisonbetweensupervisedandunsupervisedlearning.ThefollowingsectionexaminesuSUSTAIN’saccountofLove’s18studythatcomparesincidentalunsupervisedlearning,intentionalunsupervisedlearning,andsupervisedclassificationlearninginacontrolledmanner.4.ComparingSupervisedandUnsupervisedLearning

TheLove18studyisuniqueinthatitspecificallyallowsforadirectcomparisonofsupervisedandunsupervisedlearning.Insupervisedlearning,thecommondepen-dentmeasureusedtoassesslearningdifficultyistrainingaccuracy.25,30However,thereisnomeasureoftrainingaccuracyinunsupervisedlearning(thereisnorightorwrongresponseoneachstudytrial).Inordertodirectlycomparelearningper-formanceacrossthesetwotypesoflearning,acomparabledependentmeasurewasdeveloped.

Toaccomplishthis,stimuliwerecreatedbyembeddingthecategorylabel(whichistypicallyaverballabelsuchascategory“A”or“B”)intoeachstimulusasafourthbinary-valuedperceptualdimension(seeTable1).Onsupervisedclassifica-tionstudyphasetrials,subjectswereshownthevalueofthefirstthreeperceptual

Table1.Thelogicalstruc-tureofTypesI,II,IVandVIclassificationproblemstestedinRef.30.

11112222112211221212121211112222112222111112122212212112

6T.M.Gureckis&B.C.Love

dimensionsandwerequeriedonthefourth.Afterresponding,thecorrectvalueofthefourthdimensionswasshown.IntheLove18study,thefourthdimension(i.e.the“category”dimension)wasthebordercolor(eitheryelloworwhite)ofageometricfigure.Subjectsindicatedwhethertheybelievedthebordercolor(notshownonthedisplay)wasyelloworwhitebasedonthethreeotherperceptualdimensions(whichwereshownonthedisplay).Afterresponding,thecompletefigurewasdisplayed.

Onunsupervisedstudyphasetrials,allfourperceptualdimensionswereshownonstudyphasetrials(thefourthdimensionwasnotqueried).Intheintentionalunsupervisedlearningcondition,subjectswereawaretheywereinalearningtaskandwereinstructedtoactivelysearchforpatternsthatcharacterizedthetrainingitems.Incontrast,subjectsintheincidentalunsupervisedlearningconditionwerenotawarethattheywereinalearningtaskandwereinstructedtosimplyratehowpleasanttheyfoundeachstimulusitem.

Ineachofthethreestudyconditions(supervisedclassificationlearning,in-tentionalunsupervisedlearning,incidentalunsupervisedlearning),subjectsweretrainedoneitherTypesI,II,IV,orVIcategorystructures(seeTable1)definedbyShepard,HovlandandJenkins.30TypeIproblemonlyrequiresattentionalongoneinputdimension,whereasTypeIIproblemrequiresattendingtotwodimensions(TypeIIisXORonthefirsttwodimensionswithanirrelevantthirddimension).ThecategoriesinTypeIIproblemhaveahighlynonlinearstructure.TypeIVre-quiresattentionalongallthreeperceptualdimensionswitheachdimensionservingasanimperfectpredictor.TypeIVisnotablebecauseitdisplaysalinearcategorystructure.TypeVIalsorequiresattentiontoallthreeperceptualdimensionsandhasnoregularitiesacrossanypairofdimensions.Inallconditions,subjectscom-pletedtenstudyblocks(ablockconsistsofthepresentationofeachstimulusiteminarandomorder).

Categorylearningperformancewasmeasuredinatestphasewhichfollowedthestudyphase.Subjectsviewedapairofstimulithatvariedonlyonthefourthdimensions(i.e.thecategorydimension).Subjectswereinstructedtochoosetheitemthatappearedduringthestudyphase(afamiliarityorrecognitionjudgment).Asintraditionalsupervisedclassificationlearningstudies,subjectscouldbasethisjudgmentontheirknowledgeoftherelationshipbetweenthecategorydimen-sionandotherdimensions(e.g.rules,correlations,etc.)aswellasonmemorizedexemplars.Love18verifiedthatthistestingprocedureyieldsperformancescoresthatcorrelatehighlywithstudyphaseaccuracyinthesupervisedcondition.Thus,testphaseaccuracycanbeusedtocomparetheabilityofsubjectstolearnineachofthethreestudyconditions.

TheresultsareshowninTable2.Theacquisitionpatternsforthethreelearningconditionsdiffersignificantly.SubjectsintheunsupervisedconditionsdidnotshowapreferenceforTypeIIcategorystructurerelativetoTypeIVstructure.Thisef-fectwasmostpronouncedintheincidentalunsupervisedlearningcondition.Oneexplanationforthisdifferencebetweentheincidentalandintentionalunsupervisedlearningconditionsisthatintentionalunsupervisedlearningtaskencouragedsub-

HumanUnsupervisedandSupervisedLearningasaQuantitativeDistinction

Table2.ThestudyphaseandtestphaseresultsfromRef.18.uSUSTAIN’sfitisshowninparentheses.

7

SupervisedClassificationTypeI0.86(0.74)TypeII0.67(0.63)TypeIV0.65(0.60)TypeVI0.59(0.56)IntentionalTypeITypeIITypeIVTypeVITypeTypeTypeType

IIIIVVI

UnsupervisedNANANANANANANANA

Learning0.(0.90)0.73(0.75)0.70(0.65)0.61(0.58)Learning0.84(0.86)0.(0.57)0.67(0.66)0.(0.50)0.850.560.670.56

(0.81)(0.51)(0.63)(0.50)

IncidentalUnsupervisedLearning

8T.M.Gureckis&B.C.Love

Table3.

uSUSTAIN’sbestfittingparametersforRef.18studies.

Learningrate

ClustercompetitionDecisionconsistencyAttentionalfocusThresholdηβdrτ0.01722.9014.4740.4750.5680.01860.60814.4422.209

0.553/0.487

HumanUnsupervisedandSupervisedLearningasaQuantitativeDistinction9

uSUSTAIN’sfitoftheLove18datasuggeststhatunsupervisedlearning,par-ticularlyincidentalunsupervisedlearning,isbestmatchedwithlinearcategorystructuresbecausetheoptimalclusteringsolutionforalinearcategorystructureinvolvesoneclusterpercategory.Ontheotherhand,nonlinearcategorystructuresarenotwellmatchedtoanunsupervisedinductiontaskbecausenonlinearcate-gorystructurescanonlybecapturedwithmultipleclusterspercategory.Whilethelinear/nonlineardistinctionhasnotprovedcriticalinsupervisedclassificationlearning,24Love18suggestedthatthedistinctionmaybemeaningfulinunsuper-visedlearning.uSUSTAIN’saccountofthedatasupportsthisconjecture.

OnecounterintuitivepredictionthatuSUSTAINmakesisthatincidentalunsupervisedlearningmaybethepreferredinductiontaskforsometasks.Inotherwords,sometimeshumansmaybebetteroffnottryingtomasterthelearningproblem.Onesuchsituationiswhennumerousstimulusdimensionsareweaklycorrelatedwithoneanother.Undersuchcircumstances,uSUSTAINpredictsthatsupervisedclassificationlearningandintentionalunsupervisedlearningwillleadtoclusteringsolutionsthatover-differentiateitemsandthereforedonotfullycapturetheintercorrelatedstructureofthecategories.Incontrast,incidentalunsupervisedlearningtendstoaggregateitemsincommonclustersandismorelikelytocap-turetheunderlyingcategorystructure.uSUSTAIN’slowersettingofτparameter(whichincreasesuSUSTAIN’stendencytoclusteritemstogether)forincidentalunsupervisedlearningdrivesthisprediction.

Despitetheapparentdifferencesbetweensupervisedclassificationlearning,intentionalunsupervisedlearningandincidentalunsupervisedlearning,allthreeinductiontasksaremodeledthroughacommonmechanisminuSUSTAIN.Beyondthecurrentproject,animportantgoalofoureffortsistomodelhumanlearningacrossarangeofsituationsandinductiontasks.Doingsohighlightstheoreticalconnectionsacrossdatasetsandshouldleadtoamoregeneralunderstandingofhumanlearning.

Acknowledgments

ThisworkwassupportedbyAFOSRGrantF49620-01-1-0295toB.C.Love.CorrespondenceconcerningthisresearchshouldbeaddressedtoToddM.Gureckis,gureckis@love.psy.utexas.edu.

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