Pattern Recognition and Machine Learning (Book Part 2).pdf

《Pattern Recognition and Machine Learning (Book Part 2).pdf》由会员上传分享，免费在线阅读，更多相关内容在学术论文-天天文库。

1、8GraphicalModelsProbabilitiesplayacentralroleinmodernpatternrecognition.WehaveseeninChapter1thatprobabilitytheorycanbeexpressedintermsoftwosimpleequationscorrespondingtothesumruleandtheproductrule.Alloftheprobabilisticinfer-enceandlearningmanipulationsdisc

2、ussedinthisbook,nomatterhowcomplex,amounttorepeatedapplicationofthesetwoequations.Wecouldthereforeproceedtoformulateandsolvecomplicatedprobabilisticmodelspurelybyalgebraicma-nipulation.However,weshallfindithighlyadvantageoustoaugmenttheanalysisusingdiagramm

3、aticrepresentationsofprobabilitydistributions,calledprobabilisticgraphicalmodels.Theseofferseveralusefulproperties:1.Theyprovideasimplewaytovisualizethestructureofaprobabilisticmodelandcanbeusedtodesignandmotivatenewmodels.2.Insightsintothepropertiesofthem

4、odel,includingconditionalindependenceproperties,canbeobtainedbyinspectionofthegraph.3593608.GRAPHICALMODELS3.Complexcomputations,requiredtoperforminferenceandlearninginsophis-ticatedmodels,canbeexpressedintermsofgraphicalmanipulations,inwhichunderlyingmath

5、ematicalexpressionsarecarriedalongimplicitly.Agraphcomprisesnodes(alsocalledvertices)connectedbylinks(alsoknownasedgesorarcs).Inaprobabilisticgraphicalmodel,eachnoderepresentsarandomvariable(orgroupofrandomvariables),andthelinksexpressprobabilisticrelation

6、-shipsbetweenthesevariables.Thegraphthencapturesthewayinwhichthejointdistributionoveralloftherandomvariablescanbedecomposedintoaproductoffactorseachdependingonlyonasubsetofthevariables.Weshallbeginbydis-cussingBayesiannetworks,alsoknownasdirectedgraphicalm

7、odels,inwhichthelinksofthegraphshaveaparticulardirectionalityindicatedbyarrows.TheothermajorclassofgraphicalmodelsareMarkovrandomfields,alsoknownasundirectedgraphicalmodels,inwhichthelinksdonotcarryarrowsandhavenodirectionalsignificance.Directedgraphsareusef

8、ulforexpressingcausalrelationshipsbetweenrandomvariables,whereasundirectedgraphsarebettersuitedtoexpressingsoftcon-straintsbetweenrandomvariables.Forthepurposesofsolvinginferenceproblems,itisoftenconvenientto