RE SS OC EURA OR TIO OCE SS IN TE IP Bayesian Surprise Attracts Human Attention Laurent - PDF document

RESSOCEURAORTIOOCE BayesianSurpriseAttractsHumanAttention LaurentIttiDepartmentofComputerScience assupportedbymountingevidenceforaroleofthehippocampusasanoveltydetector[19,20,21].Finally,seekingnoveltyisawell-identiedhumancharactertrait,withpossibleassociationwiththedopamineD4receptorgene[22,23,24].IntheBayesianframework,wedeveloptheonlyconsistenttheoryofsurprise,intermsofthedifferencebetweentheposteriorandpriordistributionsofbeliefsofanobserverovertheavailableclassofmodelsorhypothesesabouttheworld.Weshowthatthisdenitionderivedfromrstprinciplespresentskeyadvantagesovermoread-hocformulations,typ-icallyrelyingondetectingoutlierstimuli.Armedwiththisnewframework,weprovidedirectexperimentalevidencethatsurprisebestcharacterizeswhatattractshumangazeinlargeamountsofnaturalvideostimuli.Wehereextendarecentpilotstudy[25],addingmorecomprehensivetheory,large-scalehumandatacollection,andadditionalanalysis.1TheoryBayesianDenitionofSurprise.Weproposethatsurpriseisageneralconcept,whichcanbederivedfromrstprinciplesandformalizedacrossspatio-temporalscales,sensorymodalities,and,moregenerally,datatypesanddatasources.Twoelementsareessentialforaprincipleddenitionofsurprise.First,surprisecanexistonlyinthepresenceofuncertainty,whichcanarisefromintrinsicstochasticity,missinginformation,orlimitedcomputingresources.Aworldthatispurelydeterministicandpredictableinreal-timeforagivenobservercontainsnosurprises.Second,surprisecanonlybedenedinarelative,subjective,mannerandisrelatedtotheexpectationsoftheobserver,beitasinglesynapse,neuronalcircuit,organism,orcomputerdevice.Thesamedatamaycarrydifferentamountofsurprisefordifferentobservers,orevenforthesameobservertakenatdifferenttimes.InprobabilityanddecisiontheoryitcanbeshownthattheonlyconsistentandoptimalwayformodelingandreasoningaboutuncertaintyisprovidedbytheBayesiantheoryofprobability[26,27,28].Furthermore,intheBayesianframework,probabilitiescorrespondtosubjectivedegreesofbeliefsinhypothesesormodelswhichareupdated,asdataisac-quired,usingBayes'theoremasthefundamentaltoolfortransformingpriorbeliefdistribu-tionsintoposteriorbeliefdistributions.Therefore,withinthesameoptimalframework,theonlyconsistentdenitionofsurprisemustinvolve:(1)probabilisticconceptstocopewithuncertainty;and(2)priorandposteriordistributionstocapturesubjectiveexpectations.ConsistentlywiththisBayesianapproach,thebackgroundinformationofanobserveriscapturedbyhis/her/itspriorprobabilitydistributionfP(M)gM2MoverthehypothesesormodelsMinamodelspaceM.Giventhispriordistributionofbeliefs,thefunda-mentaleffectofanewdataobservationDontheobserveristochangethepriordistri-butionfP(M)gM2MintotheposteriordistributionfP(MjD)gM2MviaBayestheorem,whereby8M2M;P(MjD)=P(DjM)P(D)P(M):(1)Inthisframework,thenewdataobservationDcarriesnosurpriseifitleavestheobserverbeliefsunaffected,thatis,iftheposteriorisidenticaltotheprior;conversely,Dissur-prisingiftheposteriordistributionresultingfromobservingDsignicantlydiffersfromthepriordistribution.Thereforeweformallymeasuresurpriseelicitedbydataassomedistancemeasurebetweentheposteriorandpriordistributions.ThisisbestdoneusingtherelativeentropyorKullback-Leibler(KL)divergence[29].Thus,surpriseisdenedbytheaverageofthelog-oddratio:S(D;M)=KL(P(MjD);P(M))=ZMP(MjD)logP(MjD)P(M)dM(2)takenwithrespecttotheposteriordistributionoverthemodelclassM.NotethatKLisnotsymmetricbuthaswell-knowntheoreticaladvantages,includinginvariancewithrespectto Figure1:Computingsurpriseinearlysensoryneurons.(a)Priordataobservations,tuningprefer-ences,andtop-downinuencescontributetoshapingasetof“priorbeliefs”aneuronmayhaveoveraclassofinternalmodelsorhypothesesabouttheworld.Forinstance,MmaybeasetofPoissonprocessesparameterizedbytherate,withfP(M)gM2M=fP()g2IR+thepriordistributionofbeliefsaboutwhichPoissonmodelswelldescribetheworldassensedbytheneuron.NewdataDupdatesthepriorintotheposteriorusingBayes'theorem.Surprisequanti®esthedifferencebe-tweentheposteriorandpriordistributionsoverthemodelclassM.Theremainingpanelsdetailhowsurprisediffersfromconventionalmodel®ttingandoutlier-basednovelty.(b)Instandardit-erativeBayesianmodel®tting,ateveryiterationN,incomingdataDNisusedtoupdatethepriorfP(MjD1;D2;:::;DN1)gM2MintotheposteriorfP(MjD1;D2;:::;DN)gM2M.Freezingthislearningatagiveniteration,onethenpicksthecurrentlybestmodel,usuallyusingeitheramaxi-mumlikelihoodcriterion,oramaximumaposteriorione(yieldingMMAPshown).(c)Thisbestmodelisusedforanumberoftasksatthecurrentiteration,includingoutlier-basednoveltydetec-tion.Newdataisthenconsiderednovelatthatinstantifithaslowlikelihoodforthebestmodel(e.g.,DbNismorenovelthanDaN).Thisfocusontothesinglebestmodelpresentsobviouslimita-tions,especiallyinsituationswhereothermodelsarenearlyasgood(e.g.,Minpanel(b)isentirelyignoredduringstandardnoveltycomputation).Onepalliativesolutionistoconsidermixturemod-els,orsimplyP(D),butthisjustamountstoshiftingtheproblemintoadifferentmodelclass.(d)Surprisedirectlyaddressesthisproblembysimultaneouslyconsideringallmodelsandbymeasuringhowdatachangestheobserver'sdistributionofbeliefsfromfP(MjD1;D2;:::;DN1)gM2MtofP(MjD1;D2;:::;DN)gM2MovertheentiremodelclassM(orangeshadedarea).reparameterizations.Aunitofsurprise—a“wow”—maythenbedenedforasinglemodelMastheamountofsurprisecorrespondingtoatwo-foldvariationbetweenP(MjD)andP(M),i.e.,aslogP(MjD)=P(M)(withlogtakeninbase2),withthetotalnumberofwowsexperiencedforallmodelsobtainedthroughtheintegrationineq.2.Surpriseandoutlierdetection.OutlierdetectionbasedonthelikelihoodP(DjMbest)ofDgivenasinglebestmodelMbestisatbestanapproximationtosurpriseand,insome cases,ismisleading.Consider,forinstance,acasewhereDhasverysmallprobabilitybothforamodelorhypothesisMandforasinglealternativehypothesisM.AlthoughDisastrongoutlier,itcarriesverylittleinformationregardingwhetherMorMisthebettermodel,andthereforeverylittlesurprise.ThusanoutlierdetectionmethodwouldstronglyfocusattentionalresourcesontoD,althoughDisafalsepositive,inthesensethatitcarriesnousefulinformationfordiscriminatingbetweenthetwoalternativehypothesesMandM.Figure1furtherillustratesthisdisconnectbetweenoutlierdetectionandsurprise.2HumanexperimentsTotestthesurprisehypothesis—thatsurpriseattractshumanattentionandgazeinnatu-ralscenes—werecordedeyemovementsfromeightna¨veobservers(threefemalesandvemales,ages23-32,normalorcorrected-to-normalvision).Eachwatchedasubsetfrom50videoclipstotalingover25minutesofplaytime(46,489videoframes,640480,60.27Hz,meanscreenluminance30cd/m2,room4cd/m2,viewingdistance80cm,eldofview2821).Clipscomprisedoutdoorsdaytimeandnighttimescenesofcrowdedenvironments,videogames,andtelevisionbroadcastincludingnews,sports,andcommer-cials.Right-eyepositionwastrackedwitha240Hzvideo-baseddevice(ISCANRK-464),withmethodsaspreviously[30].Twohundredcalibratedeyemovementtraces(10,192saccades)wereanalyzed,correspondingtofourdistinctobserversforeachofthe50clips.Figure2showssamplescanpathsforonevideoclip.Tocharacterizeimageregionsselectedbyparticipants,weprocessvideoclipsthroughcom-putationalmetricsthatoutputatopographicdynamicmasterresponsemap,assigninginreal-timearesponsevaluetoeveryinputlocation.Agoodmastermapwouldhighlight,morethanexpectedbychance,locationsgazedtobyobservers.Toscoreeachmetricwehencesample,atonsetofeveryhumansaccade,mastermapactivityaroundthesaccade'sfutureendpoint,andaroundauniformlyrandomendpoint(randomsamplingwasrepeated100timestoevaluatevariability).WequantifydifferencesbetweenhistogramsofmasterFigure2:(a)Sampleeyemovementtracesfromfourobservers(squaresde-notesaccadeendpoints).(b)Ourdataexhibitshighinter-individualoverlap,shownherewiththelocationswhereonehumansaccadeendpointwasnearby(5)one(whitesquares),two(cyansquares),orallthree(blacksquares)otherhumans.(c)Ametricwherethemastermapwascreatedfromthethreeeyemovementtracesotherthanthatbe-ingtestedyieldsanupper-boundKLscore,computedbycomparingthehis-togramsofmetricvaluesathuman(nar-rowbluebars)andrandom(widergreenbars)saccadetargets.Indeed,thismet-ric'smapwasverysparse(manyrandomsaccadeslandingonlocationswithnear-zeroresponse),yethumanspreferen-tiallysaccadedtowardsthethreeactivehotspotscorrespondingtotheeyeposi-tionsofthreeotherhumans(manyhu-mansaccadeslandingonlocationswithnear-unityresponses). mapsamplescollectedfromhumanandrandomsaccadesusingagaintheKullback-Leibler(KL)distance:metricswhichbetterpredicthumanscanpathsexhibithigherdistancesfromrandomas,typically,observersnon-uniformlygazetowardsaminorityofregionswithhighestmetricresponseswhileavoidingamajorityofregionswithlowmetricresponses.Thisapproachpresentsseveraladvantagesoversimplerscoringschemes[31,32],includ-ingagnosticitytoputativemechanismsforgeneratingsaccadesandthefactthatapplyinganycontinuousnonlinearitytomastermapvalueswouldnotaffectscoring.Experimentalresults.Wetestsixcomputationalmetrics,encompassingandextendingthestate-of-the-artfoundinpreviousstudies.Therstthreequantifystaticimageproperties(localintensityvariancein1616imagepatches[31];localorientededgedensityasmeasuredwithGaborlters[33];andlocalShannonentropyin1616imagepatches[34]).Theremainingthreemetricsaremoresensitivetodynamicevents(localmotion[33];outlier-basedsaliency[33];andsurprise[25]).Forallmetrics,wendthathumansaresignicantlyattractedbyimageregionswithhighermetricresponses.However,thestaticmetricstypicallyrespondvigorouslyatnumerousvi-suallocations(Figure3),hencetheyarepoorlyspecicandyieldrelativelylowKLscoresbetweenhumansandrandom.Themetricssensitivetomotion,outliers,andsurprisingevents,incomparison,yieldsparsermapsandhigherKLscores.Thesurprisemetricofinterestherequantieslow-levelsurpriseinimagepatchesoverspaceandtime,andatthispointdoesnotaccountforhigh-levelorcognitivebeliefsofourhumanobservers.Rather,itassumesafamilyofsimplemodelsforimagepatches,eachprocessedthrough72earlyfeaturedetectorssensitivetocolor,orientation,motion,etc.,andcomputessurprisefromshiftsinthedistributionofbeliefsaboutwhichmodelsbetterdescribethepatches(see[25]and[35]fordetails).Wendthatthesurprisemetricsig-nicantlyoutperformsallothercomputationalmetrics(p10100orbetteront-testsforequalityofKLscores),scoringnearly20%betterthanthesecond-bestmetric(saliency)and60%betterthanthebeststaticmetric(entropy).Surprisingstimulioftensubstantiallydifferfromsimplefeatureoutliers;forexample,acontinuallyblinkinglightonastaticbackgroundelicitssustainedickerduetoitslocallyoutliertemporaldynamicsbutisonlysurprisingforamoment.Similarly,ashowerofrandomly-coloredpixelscontinuallyex-citesalllow-levelfeaturedetectorsbutrapidlybecomesunsurprising.Strongestattractorsofhumanattention.Clearly,inourandpreviouseye-trackingex-periments,insomesituationspotentiallyinterestingtargetsweremorenumerousthaninothers.Withmanypossibletargets,differentobserversmayorienttowardsdifferentloca-tions,makingitmoredifcultforasinglemetrictoaccuratelypredictallobservers.Henceweconsider(Figure4)subsetsofhumansaccadeswhereatleasttwo,three,orallfourobserverssimultaneouslyagreedonagazetarget.Observerscouldhaveagreedbasedonbottom-upfactors(e.g.,onlyonelocationhadinterestingvisualappearanceatthattime),top-downfactors(e.g.,onlyoneobjectwasofcurrentcognitiveinterest),orboth(e.g.,asinglecognitivelyinterestingobjectwaspresentwhichalsohaddistinctiveappearance).Irrespectivelyofthecauseforagreement,itindicatesconsolidatedbeliefthatalocationwasattractive.WhiletheKLscoresofallmetricsimprovedwhenprogressivelyfocusingontoonlythoselocations,dynamicmetricsimprovedmoresteeply,indicatingthatstimuliwhichmorereliablyattractedallobserverscarriedmoremotion,saliency,andsurprise.Surpriseremainedsignicantlythebestmetrictocharacterizetheseagreed-uponattractorsofhumangaze(p10100orbetteront-testsforequalityofKLscores).Overall,surpriseexplainedthegreatestfractionofhumansaccades,indicatingthathumansaresignicantlyattractedtowardssurprisinglocationsinvideodisplays.Over72%ofallhumansaccadesweretargetedtolocationspredictedtobemoresurprisingthanonaverage.Whenonlyconsideringsaccadeswheretwo,three,orfourobserversagreedonacommongazetarget,thisgureroseto76%,80%,and84%,respectively. Figure3:(a)Samplevideoframes,withcorrespondinghumansaccadesandpredictionsfromtheentropy,surprise,andhuman-derivedmetrics.Entropymaps,likeintensityvarianceandorientationmaps,exhibitedmanylocationswithhighresponses,hencehadlowspeci®cityandwerepoorlydiscriminative.Incontrast,motion,saliency,andsurprisemapsweremuchsparserandmorespeci®c,withsurprisesigni®cantlymoreoftenontarget.Forthreeexampleframes(®rstcolumn),saccadesfromonesubjectareshown(arrows)withcorrespondingaperturesoverwhichmastermapactivityatthesaccadeendpointwassampled(circles).(b)KLscoresforthesemetricsindicatesigni®cantlydifferentperformancelevels,andastrictrankingofvarianceorientationentropymotionsaliencysurprisehuman-derived.KLscoreswerecomputedbycomparingthenumberofhumansaccadeslandingontoeachgivenrangeofmastermapvalues(narrowbluebars)tothenumberofrandomsaccadeshittingthesamerange(widergreenbars).Ascoreofzerowouldindicateequalitybetweenthehumanandrandomhistograms,i.e.,humansdidnottendtohitvariousmastermapvaluesanydifferentlyfromexpectedbychance,or,themastermapcouldnotpredicthumansaccadesbetterthanrandomsaccades.Amongthesixcomputationalmetricstestedintotal,surpriseperformedbest,inthatsurprisinglocationswererelativelyfewyetreliablygazedtobyhumans. Figure4:KLscoreswhenconsideringonlysaccadeswhereatleastone(all10,192saccades),two(7,948saccades),three(5,565saccades),orallfour(2,951saccades)humansagreedonacommongazelocation,forthestatic(a)anddynamicmetrics(b).Staticmetricsimprovedsubstantiallywhenprogressivelyfocusingontosaccadeswithstrongerinter-observeragreement(averageslope0:560:37percentKLscoreunitsper1,000prunedsaccades).Hence,whenhumansagreedonalocation,theyalsotendedtobemorereliablypredictedbythemetrics.Furthermore,dynamicmetricsimproved4:5timesmoresteeply(slope2:440:37),suggestingastrongerroleofdynamiceventsinattractinghumanattention.Surprisingeventsweresigni®cantlythestrongest(t-testsforequalityofKLscoresbetweensurpriseandothermetrics,p10100).3DiscussionWhilepreviousresearchhasshownwitheitherstaticscenesordynamicsyntheticstimulithathumanspreferentiallyxateregionsofhighentropy[34],contrast[31],saliency[32],icker[36],ormotion[37],ourdataprovidesdirectexperimentalevidencethathumansxatesurprisinglocationsevenmorereliably.Theseconclusionsweremadepossiblebydevelopingnewtoolstoquantifywhatattractshumangazeoverspaceandtimeindynamicnaturalscenes.Surpriseexplainedbestwherehumanslookwhenconsideringallsaccades,andevenmoresowhenrestrictingtheanalysistoonlythosesaccadesforwhichhumanobserverstendedtoagree.Surprisehencerepresentsaninexpensive,easilycomputableapproximationtohumanattentionalallocation.Intheabsenceofquantitativetoolstomeasuresurprise,mostexperimentalandmodelingworktodatehasadoptedtheapproximationthatnoveleventsaresurprising,andhasfo-cusedonexperimentalscenarioswhicharesimpleenoughtoensureanoverlapbetweeninformalnotionsofnoveltyandsurprise:forexample,astimulusisnovelduringtestingifithasnotbeenseenduringtraining[9].Ourdenitionopensnewavenuesformoresophis-ticatedexperiments,wheresurpriseelicitedbydifferentstimulicanbepreciselycomparedandcalibrated,yieldingpredictionsatthesingle-unitaswellasbehaviorallevels.Thedenitionofsurprise—asthedistancebetweentheposteriorandpriordistributionsofbeliefsovermodels—isentirelygeneralandreadilyapplicabletotheanalysisofaudi-tory,olfactory,gustatory,orsomatosensorydata.Whileherewehavefocusedonbehaviorratherthandetailedbiophysicalimplementation,itisworthnotingthatdetectingsurpriseinneuralspiketrainsdoesnotrequiresemanticunderstandingofthedatacarriedbythespiketrains,andthuscouldprovideguidingsignalsduringself-organizationanddevelopmentofsensoryareas.Athigherprocessinglevels,top-downcuesandtaskdemandsareknowntocombinewithstimulusnoveltyincapturingattentionandtriggeringlearning[1,38],ideaswhichmaynowbeformalizedandquantiedintermsofpriors,posteriors,andsurprise.Surprise,indeed,inherentlydependsonuncertaintyandonpriorbeliefs.Hencesurprisetheorycanfurtherbetestedandutilizedinexperimentswherethepriorisbiased,forex- amplebytop-downinstructionsorpriorexposurestostimuli[38].Inaddition,simplesurprise-basedbehavioralmeasuressuchastheeye-trackingoneusedheremayproveuse-fulforearlydiagnosticofhumanconditionsincludingautismandattention-decithyper-activedisorder,aswellasforquantitativecomparisonbetweenhumansandanimalswhichmayhavelowerordifferentpriors,includingmonkeys,frogs,andies.Beyondsensorybiology,computablesurprisecouldguidethedevelopmentofdataminingandcompres-sionsystems(givingmorebitstosurprisingregionsofinterest),tondsurprisingagentsincrowds,surprisingsentencesinbooksorspeeches,surprisingsequencesingenomes,sur-prisingmedicalsymptoms,surprisingodorsinairportluggageracks,surprisingdocumentsontheworld-wide-web,ortodesignsurprisingadvertisements.Acknowledgments:SupportedbyHFSP,NSFandNGA(L.I.),NIHandNSF(P.B.).WethankUCI'sInstituteforGenomicsandBioinformaticsandUSC'sCenterHighPerformanceComputingandCommunications(www.usc.edu/hpcc)foraccesstotheircomputingclusters.References[1]Ranganath,C.&Rainer,G.NatRevNeurosci4,193–202(2003).[2]Rao,R.P.&Ballard,D.H.NatNeurosci2,79–87(1999).[3]Olshausen,B.A.&Field,D.J.Nature381,607–609(1996).[4]M¨uller,J.R.,Metha,A.B.,Krauskopf,J.&Lennie,P.Science285,1405–1408(1999).[5]Dragoi,V.,Sharma,J.,Miller,E.K.&Sur,M.NatNeurosci5,883–891(2002).[6]David,S.V.,Vinje,W.E.&Gallant,J.L.JNeurosci24,6991–7006(2004).[7]Maffei,L.,Fiorentini,A.&Bisti,S.Science182,1036–1038(1973).[8]Movshon,J.A.&Lennie,P.Nature278,850–852(1979).[9]Fecteau,J.H.&Munoz,D.P.NatRevNeurosci4,435–443(2003).[10]Kurahashi,T.&Menini,A.Nature385,725–729(1997).[11]Bradley,J.,Bonigk,W.,Yau,K.W.&Frings,S.NatNeurosci7,705–710(2004).[12]Ulanovsky,N.,Las,L.&Nelken,I.NatNeurosci6,391–398(2003).[13]Solomon,S.G.,Peirce,J.W.,Dhruv,N.T.&Lennie,P.Neuron42,155–162(2004).[14]Smirnakis,S.M.,Berry,M.J.&etal.Nature386,69–73(1997).[15]Brown,S.P.&Masland,R.H.NatNeurosci4,44–51(2001).[16]Kennedy,H.J.,Evans,M.G.&etal.NatNeurosci6,832–836(2003).[17]Schultz,W.&Dickinson,A.AnnuRevNeurosci23,473–500(2000).[18]Fletcher,P.C.,Anderson,J.M.,Shanks,D.R.etal.NatNeurosci4,1043–1048(2001).[19]Knight,R.Nature383,256–259(1996).[20]Stern,C.E.,Corkin,S.,Gonzalez,R.G.etal.ProcNatlAcadSciUSA93,8660–8665(1996).[21]Li,S.,Cullen,W.K.,Anwyl,R.&Rowan,M.J.NatNeurosci6,526–531(2003).[22]Ebstein,R.P.,Novick,O.,Umansky,R.etal.NatGenet12,78–80(1996).[23]Benjamin,J.,Li,L.&etal.NatGenet12,81–84(1996).[24]Lusher,J.M.,Chandler,C.&Ball,D.MolPsychiatry6,497–499(2001).[25]Itti,L.&Baldi,P.InProc.IEEECVPR.SanSiego,CA(2005inpress).[26]Cox,R.T.Am.J.Phys.14,1–13(1964).[27]Savage,L.J.Thefoundationsofstatistics(Dover,NewYork,1972).(FirstEditionin1954).[28]Jaynes,E.T.ProbabilityTheory.TheLogicofScience(CambridgeUniversityPress,2003).[29]Kullback,S.InformationTheoryandStatistics(Wiley,NewYork:NewYork,1959).[30]Itti,L.VisualCognition(2005inpress).[31]Reinagel,P.&Zador,A.M.Network10,341–350(1999).[32]Parkhurst,D.,Law,K.&Niebur,E.VisionRes42,107–123(2002).[33]Itti,L.&Koch,C.NatRevNeurosci2,194–203(2001).[34]Privitera,C.M.&Stark,L.W.IEEETransPattAnalMachIntell22,970–982(2000).[35]Allsourcecodeforallmetricsisfreelyavailableathttp://iLab.usc.edu/toolkit/.[36]Theeuwes,J.PerceptPsychophys57,637–644(1995).[37]Abrams,R.A.&Christ,S.E.PsycholSci14,427–432(2003).[38]Wolfe,J.M.&Horowitz,T.S.NatRevNeurosci5,495–501(2004).