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1、AnintroductiontographicalmodelsKevinP.Murphy10May20011IntroductionThefollowingquotation,fromthePrefaceof[Jor99],providesaveryconciseintroductiontographicalmodels.Graphicalmodelsareamarriagebetweenprobabilitytheoryandgraphtheory.Theyprovideanaturaltoolfordealingwithtwoproblemstha
2、toccurthroughoutappliedmathematicsandengineering{uncertaintyandcomplexity{andinparticulartheyareplayinganincreasinglyimportantroleinthedesignandanalysisofmachinelearningalgorithms.Fundamentaltotheideaofagraphicalmodelisthenotionofmodularity{acomplexsystemisbuiltbycombiningsimple
3、rparts.Probabilitytheoryprovidesthegluewherebythepartsarecombined,ensuringthatthesystemasawholeisconsistent,andprovidingwaystointerfacemodelstodata.Thegraphtheoreticsideofgraphicalmodelsprovidesbothanintuitivelyappealinginterfacebywhichhumanscanmodelhighly-interactingsetsofvaria
4、blesaswellasadatastructurethatlendsitselfnaturallytothedesignofecientgeneral-purposealgorithms.Manyoftheclassicalmultivariateprobabalisticsystemsstudiedin eldssuchasstatistics,systemsengineering,informationtheory,patternrecognitionandstatisticalmechanicsarespecialcasesofthegene
5、ralgraphicalmodelformalism{examplesincludemixturemodels,factoranalysis,hiddenMarkovmodels,Kalman ltersandIsingmodels.Thegraphicalmodelframeworkprovidesawaytoviewallofthesesystemsasinstancesofacommonunderlyingformalism.Thisviewhasmanyadvantages{inparticular,specializedtechniquest
6、hathavebeendevelopedinone eldcanbetransferredbetweenresearchcommunitiesandexploitedmorewidely.Moreover,thegraphicalmodelformalismprovidesanaturalframeworkforthedesignofnewsystems.Inthispaper,wewill
eshoutthisremarkbydiscussingthefollowingtopics:Representation:howcanagraphicalmo
7、delcompactlyrepresentajointprobabilitydistribution?Inference:howcanweecientlyinferthehiddenstatesofasystem,givenpartialandpossiblynoisyobservations?Learning:howdoweestimatetheparametersandstructureofthemodel?Decisiontheory:whathappenswhenitistimetoconvertbeliefsintoactions?
8、Applications:whathasthismachinerybeenusedfor?1P
