Hammersley Clifford定理12页精选文档Word下载.docx
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Hammersley Clifford定理12页精选文档Word下载.docx
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其实,任何一门学科都离不开死记硬背,关键是记忆有技巧,“死记”之后会“活用”。
不记住那些基础知识,怎么会向高层次进军?
尤其是语文学科涉猎的范围很广,要真正提高学生的写作水平,单靠分析文章的写作技巧是远远不够的,必须从基础知识抓起,每天挤一点时间让学生“死记”名篇佳句、名言警句,以及丰富的词语、新颖的材料等。
这样,就会在有限的时间、空间里给学生的脑海里注入无限的内容。
日积月累,积少成多,从而收到水滴石穿,绳锯木断的功效。
TherelationshipbetweenMarkovandGibbsrandomfieldswasinitiatedbyRolandDobrushin[1]andFrankSpitzer[2]inthecontextofstatisticalmechanics.ThetheoremisnamedafterJohnHammersleyandPeterCliffordwhoprovedtheequivalenceinanunpublishedpaperin1971.[3][4]Simplerproofsusingtheinclusion-exclusionprincipleweregivenindependentlybyGeoffreyGrimmett,[5]Preston[6]andSherman[7]in1973,withafurtherproofbyJulianBesagin1974.[8]
“师”之概念,大体是从先秦时期的“师长、师傅、先生”而来。
其中“师傅”更早则意指春秋时国君的老师。
《说文解字》中有注曰:
“师教人以道者之称也”。
“师”之含义,现在泛指从事教育工作或是传授知识技术也或是某方面有特长值得学习者。
“老师”的原意并非由“老”而形容“师”。
“老”在旧语义中也是一种尊称,隐喻年长且学识渊博者。
“老”“师”连用最初见于《史记》,有“荀卿最为老师”之说法。
慢慢“老师”之说也不再有年龄的限制,老少皆可适用。
只是司马迁笔下的“老师”当然不是今日意义上的“教师”,其只是“老”和“师”的复合构词,所表达的含义多指对知识渊博者的一种尊称,虽能从其身上学以“道”,但其不一定是知识的传播者。
今天看来,“教师”的必要条件不光是拥有知识,更重于传播知识。
Notes
^Dobrushin,P.L.(1968),"
TheDescriptionofaRandomFieldbyMeansofConditionalProbabilitiesandConditionsofItsRegularity"
TheoryofProbabilityanditsApplications13
(2):
197–224,doi:
10.1137/1113026,Spitzer,Frank(1971),"
MarkovRandomFieldsandGibbsEnsembles"
TheAmericanMathematicalMonthly78
(2):
142–154,doi:
10.2307/2317621,JSTOR2317621,Hammersley,J.M.;
Clifford,P.(1971),Markovfieldsonfinitegraphsandlattices,Clifford,P.(1990),"
Markovrandomfieldsinstatistics"
inGrimmett,G.R.;
Welsh,D.J.A.,DisorderinPhysicalSystems:
AVolumeinHonourofJohnM.Hammersley,OxfordUniversityPress,pp.19–32,ISBN0198532156,MR1064553,retrieved2009-05-04^Grimmett,G.R.(1973),"
Atheoremaboutrandomfields"
BulletinoftheLondonMathematicalSociety5
(1):
81–84,doi:
10.1112/blms/5.1.81,MR0329039^Preston,C.J.(1973),"
GeneralizedGibbsstatesandMarkovrandomfields"
AdvancesinAppliedProbability5
(2):
242–261,doi:
10.2307/1426035,JSTOR1426035,MR0405645.JSTOR1426035,Sherman,S.(1973),"
MarkovrandomfieldsandGibbsrandomfields"
IsraelJournalofMathematics14
(1):
92–103,doi:
10.1007/BF02761538,MR0321185^Besag,J.(1974),"
Spatialinteractionandthestatisticalanalysisoflatticesystems"
JournaloftheRoyalStatisticalSociety.SeriesB(Methodological)36
(2):
192–236,MR0373208.JSTOR2984812FurtherreadingBilmes,Jeff(Spring2019),Handout2:
Hammersley–Clifford,coursenotesfromUniversityofWashingtoncourse.Grimmett,Geoffrey,ProbabilityonGraphs,Chapter7,Helge,TheHammersley–CliffordTheoremanditsImpactonModernStatistics,probability-relatedarticleisastub.YoucanhelpWikipediabyexpandingit.
Retrievedfrom"
–Clifford_theorem"
FromWikipedia,thefreeencyclopediaThefirstafternoonofthememorialsessionforJulianBesaginBristolwasanintenseandattimesemotionalmoment,wherefriendsandcolleaguesofJuliansharedmemoriesandstories.Thiscollectionoftributesshowedhowmuchofalarger-than-lifecharacterhewas,fromhislong-termedandwide-rangedimpactonstatisticstohisveryhighexpectations,bothforhimselfandforothers,leadingtoatotalanduncompromisingresearchethics,tohispassionfor[extreme]sportsandoutdoors.(Thestoriesduringandafterdinerwereofamorepersonalnature,butatleastasmuchenjoyable!
)ThetalksontheseconddayshowedhowmuchandhowdeeplyJulianhadcontributedtospatialstatisticsandagriculturalexperiments,topseudo-likelihood,toMarkovrandomfieldsandimageanalysis,andtoMCMCmethodologyandpractice.IhopeIdidnotbotchtoomuchmypresentationonthehistoryofMCMC,whileIfoundreadingthroughthe1974,1986and1993ReadPapersandtheirdiscussionsanimmenselyrewardingexperiment(IwishIhaddonepriortocompletingourStatisticalSciencepaper,butitwasboundtobeincompletebynature!
).SomeinterestinglinksmadebytheaudiencewerethepriorpublicationofproofsoftheHammersley-Cliffordtheoremin1973(byGrimmet,Preston,andSteward,respectively),aswellastheproposalofaGibbssamplerbyBrianRipleyasearlyas1977(eventhoughHastingsdiduseGibbsstepsinoneofhisexamples).ChristopheAndrieualsopointedouttomeaveryearlyMonteCarloreviewbyJohnHaltoninthe1970SIAMRewiew,reviewthatIwillread(andcommment)assoonaspossible.Overall,IamquitegladIcouldtakepartinthismemorialandIamgratefultobothPetersfororganisingitasafittingtributetoJulian.MarkovChainMonteCarlo(MCMC)methodsarecurrentlyaveryactivefieldofresearch.MCMCmethodsaresamplingmethods,basedonMarkovChainswhichareergodicwithrespecttothetargetprobabilitymeasure.Theprincipleofadaptivemethodsistooptimizeontheflysomedesignparametersofthealgorithmwithrespecttoagivencriterionreflectingthesampler'
sperformance(optimizetheacceptancerate,optimizeanimportancesamplingfunction,etc…).ApostdoctoralpositionisopenedtoworkonthenumericalanalysisofadaptiveMCMCmethods:
convergence,numericalefficiency,developmentandanalysisofnewalgorithms.Aparticularemphasiswillbegiventoapplicationsinstatisticsandmoleculardynamics.(Detaileddescription)PositionfundedbytheFrenchNationalResearchAgency(ANR)throughthe2009-2019projectANR-08-BLAN-0218.Thepositionwillbenefitfromaninterdisciplinaryenvironmentinvolvingnumericalanalysts,statisticiansandprobabilists,andofstronginteractionsbetweenthepartnersoftheprojectANR-08-BLAN-021InthemostrecentissueofStatisticalScience,thespecialtopicis"
CelebratingtheEMAlgorithm'
sQuandunciacentennial"
.ItcontainsanhistoricalsurveybyMartinTannerandWingWongontheemergenceofMCMCBayesiancomputationinthe1980′s,Thissurveyismorefocusedandmoreinformativethanourglobalhistory(alsotoappearinStatisticalScience).Inparticular,itprovidestheauthors'
analysisastowhyMCMCwasdelayedbytenyearsorso(orevenmorewhenconsideringthataGibbssamplerasasimulationtoolappearsinbothHastings'
(1970)andBesag'
s(1974)papers).Theydismiss[our]concernsaboutcomputingpower(IwasrunningMonteCarlosimulationsonmyAppleIIeby1986andasinglemeansquareerrorcurveevaluationforaJames-Steintypeestimatorwouldthentakeclosetoaweekend!
)andMarkovinnumeracy,ratherattributingthereluctancetoalackofconfidenceintothemethod.Thisperspectiveremainsdebatableas,apartfromTonyO'
HaganwhowasthenfightingagainMonteCarlomethodsasbeingun-Bayesian(1987,JRSSD),IdonotrememberanynegativeattitudeatthetimeaboutsimulationandtheimmediatespreadoftheMCMCmethodsfromAlanGelfand'
sandAdrianSmith'
spresentationsoftheir1990papershowsontheoppositethattheBayesiancommunitywasreadyforthemove.
AnotherinterestingpointmadeinthishistoricalsurveyisthatMetropolis'
andotherMarkovchainmethodswerefirstpresentedoutsidesimulationsectionsofbookslikeHammersleyandHandscomb(1964),Rubinstein(1981)andRipley(1987),perpetuatingtheimpressionthatsuchmethodsweremostlyoptimisationornichespecificmethods.ThisisalsowhyBesag'
searlierworks(notmentionedinthissurvey)didnotgetwiderrecognition,untillater.SomethingIwasnotawareistheappearanceofiterativeadaptiveimportancesampling(i.e.populationMonteCarlo)intheBayesianliteratureofthe1980′s,withproposalsfromHermanvanDijk,AdrianSmith,andothers.TheappendixaboutSmithetal.(1985),the1987specialissueofJRSSD,andthecomputationcontentsofValencia3(thatIsadlymissedforbeingintheArmy!
)isalsoquiteinformativeabouttheperceptionofcomputationalBayesianstatisticsatthistime.
AmissingconnectioninthissurveyisGillesCeleuxandJeanDiebolt'
sstochasticEM(orSEM).Asearlyas1981,withMichelBroniatowski,theyproposedasimulatedversionofEMformixtureswherethelatentvariablezwassimulatedfromitsconditionaldistributionratherthanreplacedwithitsexpectation.SothiswasthefirsthalfoftheGibbssamplerformixtureswecompletedwithJeanDieboltabouttenyearslater.(AlsofoundinGelmanandKing,1990.)Theseauthorsdidnotgetmuchrecognitionfromthecommunity,though,astheyfocusedalmostexclusivelyonmixtures,usedsimulationtoproducearandomnessthatwouldescapethelocalmodeattraction,ratherthantargetingtheposteriordistribution,anddidnotanalysetheMarkoviannatureoftheiralgorithmuntillaterwiththesimulatedannealingEMalgorithm.
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概率图模型分为有向和无向的模型。
有向的概率图模型主要包括贝叶斯网络和隐马尔可夫模型,无向的概率图模型则主要包括马尔可夫随机场模型和条件随机场模型。
2019年,卡耐基.梅隆大学的Lafferty教授(JohnLafferty,AndrewMcCallum,FernandoPereira)等针对序列数据处理提出了CRF模型(ConditionalRandomFieldsProbabilisticModelsforSegmentingandLabelingSequenceData)。
这种模型直接对后验概率建模,很好地解决了MRF模型利用多特征时需要复杂的似然分布建模以及不能利用观察图像中上下文信息的问题。
Kumar博士在2019年将CRF模型扩展到2-维格型结构,开始将其引入到图像分析领域,吸引了学术界的高度关注。
对给定观察图像,估计对应的标记图像y观察图像,x未知的标记图像
1.如果直接对后验概率建模(即考虑公式中的第一项),可以得到判别的(Discriminative)概率框架。
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