The Design and Implementation of an Interactive Le

TheDesignandImplementationofanInteractiveLearningToolforStatisticalReasoningwithUncertaintyDeborahA.VastolaandEllenL.WalkerDepartmentofComputerScience,RensselaerPolytechnicInstitute,Troy,NY12180email:[e-mail],[e-mail]:518-276-40331IntroductionStatisticalreasoningwithuncertaintyisatopicthatisgenerallycoveredinanintroductorycollegelevelcourseinArticialIntelligenceandisparticularlyrelevanttoexpertsystemsinAI.Itspurposeistoarriveatadegreeofbeliefinoneormorehypotheses,basedonincompleteoruncertaindata(evidence).Unfortunately,theconceptsofstatisticalreasoningwithuncertaintycanseemasambiguoustostudentsasthedataonwhichtheywereintendedtowork.Wedescribeaframework,intheformofaninteractivetool,tohelpstudentslearnaboutthepowerandlimitationsofreasoningwithuncertainty.Therearenumerousreasoningwithuncertaintymodels[7].WechosetofocusontheDempster-Shafermodel[9].Butsinceweproposeagenericframeworkforlearningreasoningwithuncertainty,ourdiscussionsarenotlimitedtoDempster-Shafertheory.Thetoolstructureandfunctionalitywasdesignedtoaccommodateadditionalmodels.Thegoalofthispaperistoservetheinterestsoftwotypesofreaders:1.Thosewhointendtoteachreasoningwithuncertainty.Wedescribeindetailtheeducationalobjectivesthathavebeenestablishedforthetool.2.Thosewhointendtodesigneducationalcomputerapplications.Wedescribetherequire-mentsanddesignprocessthatmustbeundertakeninordertocreateacomputertoolthateectivelycommunicatestheeducationalobjectives.Foramoredetaileddiscourseonourdevelopmentprocess,includingadiscussionofcodere-use,choosingagraphicspackage,conductingusabilityreviews,andshowingtheresultsofthosereviews,referto[11].2EducationalObjectivesTherststepindevelopingatoolwastoaddresstheissueofwhymanystudentshavedicultyunderstandingreasoningwithuncertainty.Theanswertothisquestionthenhelpedusformulate1LearningToolforReasoningwithUncertainty2theeducationalobjectivesforthetool,andtheobjectives,inturn,dictatedhowthetoolshouldlookandfeel(i.e.,theframework).Whileitistruethatreasoningwithuncertaintycanbecomplex,ourownexperiencesinlearningthematerialindicatethatthedicultyinlearningthetopicdoesnotmerelylieinitscomplexity.Thecauseisreallytwo-fold.Onecanbecharacterizedasaproblemoffoundation;theotherasaproblemofpresentation:1.Reasoningwithuncertaintyrequiressomeknowledgeandeasewithprobability.Studentsshouldhavesomeinitialexperienceinelementalprobabilitytheoryinordertotrulyun-derstanduncertaintymodels.yProbabilityistherootofreasoningwithuncertainty;mostmodelsareeitherextensionsoforcalculateddeviationsfromprobability.Basicideasaboutwaysevidenceiscombined,disjointness,intersectionandthemeaningsoftermslike\mostprobableand\lessplausiblearenecessaryfoundations.2.Textbookswesurveyedgenerallylackaconceptualpresentationtoreasoningwithuncer-tainty.Theseintroductory-levelmaterialseithergiveonlycursoryoverviewsofvariousmodelsortheyconcentrateonthenitty-grittydetails,i.e.,thealgorithmandmechanicsforgeneratingnumbers.Thereislittlefocusontheconceptsthatdierentiateonemodelfromtheother,otherthanbyvirtueofthealgorithmstheyuse.Thistendstoleavetheimpressionthatreasoningwithuncertaintyisajumbledbagoftricks.Ontheotherhand,advancedmaterialdoestendtofocusonconcepts,includingdierentiation,butinamuchmoreesotericmannerthanwouldbeappropriateforanintroductoryAIcourse[9][6].Itisunreasonabletoexpectstudentstobemastersofprobability(ortodigestadvancedmaterialinthecourseallocationoftimeforthistopic),sothetoolmustestablishabasicfoundation.Also,sincewerecognizethatstudentswon’tlikelyremembertheexactalgorithmsforeachmodelayearfromtakingthecourse,thetoolmustconcentrateonpresentingthoseconceptsthatcanandshouldberemembered.Afterstudyingprobability[1][4],analyzingadvancedmaterialonDempster-Shafer[9],anddissectingthealgorithmsofseveralmodels[7],wedevelopedthethemesitemizedbelow.Wewereconvincedthatatooldesignedforthesethemeswouldprovidethestudentsameaningfulandlastinglearningexperienceinreasoningwithuncertainty:1.Reasoningwithuncertaintyisanaturalprocessofthedynamicstateoftheworldwelivein.Ourbeliefsevolveaswelearnmoreabouttheworld.Someofourbeliefsgrowaswegetmoreevidence;someofourbeliefsareretracted.2.Weusetermslikebelief,likelihood,probably,plausiblebecausetheevidenceitselfcarriesmeasuresofuncertainty(notonlybecausewemaynothavealltheevidenceatapointintime).3.Theinformationthatwegatherandthebeliefsthatarederivedareusedtomakedecisions.4.Thosedecisionsarenotalwaysclearcut;reasoningmodelscanbeapowerfulaidtohumanjudgment/expertise,butnotamechanismtosupplantthehumanfactor(notyetanyway).Therstauthorwasnewtothetopicarea.yThetermprobabilityreferstothemathematicalrulesofprobabilitytheoryandboththeobjectiveandsubjectiveviewsofprobability.LearningToolforReasoningwithUncertainty35.Thereisatradeobetweenthecostofgatheringevidence(e.g.,makingtests)andthecostofmakingthewrongdecisionbasedupontheamountofevidencewechoosetogather.6.EachspecicmodelhasitsownkeyconceptsandacontextwithinwhichtocomparethemodelwithprobabilityandBayesreasoning[6].7.Eachmodelhasitsownalgorithmforderivingbeliefs.Wewil