bayesian reasoning and machine learning (2012)

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1、BayesianReasoningandMachineLearningDavidBarberc2007,2008,2009,2010,2011,2012NotationListVacalligraphicsymboltypicallydenotesasetofrandomvariables........7dom(x)Domainofavariable....................................................7x=xThevariablexisinthestatex.....

2、.....................................7p(x=tr)probabilityofevent/variablexbeinginthestatetrue...................7p(x=fa)probabilityofevent/variablexbeinginthestatefalse...................7p(x;y)probabilityofxandy...................................................8

3、p(xy)probabilityofxandy...................................................8p(x[y)probabilityofxory....................................................8p(xjy)Theprobabilityofxconditionedony...................................8X??YjZVariablesXareindependentofvariab

4、lesYconditionedonvariablesZ.11X>>YjZVariablesXaredependentonvariablesYconditionedonvariablesZ..11RRForcontinuousvariablesthisisshorthandforf(x)dxandfordiscretevari-f(x)Pxablesmeanssummationoverthestatesofx,f(x)..................17xI[S]Indicator:hasvalue1ifthestat

5、ementSistrue,0otherwise..........19pa(x)Theparentsofnodex.................................................26ch(x)Thechildrenofnodex.................................................26ne(x)Neighboursofnodex..................................................26dim(x)F

6、oradiscretevariablex,thisdenotesthenumberofstatesxcantake..34hf(x)iTheaverageofthefunctionf(x)withrespecttothedistributionp(x).158p(x)Deltafunction.Fordiscretea,b,thisistheKroneckerdelta,a;bandfor(a;b)continuousa,btheDiracdeltafunction(ab)....................

7、..160dimxThedimensionofthevector/matrixx................................171](x=s;y=t)Thenumberoftimesxisinstatesandyinstatetsimultaneously...195]xyThenumberoftimesvariablexisinstatey..........................273DDataset............................................

8、...................285nDataindex...........................................................285NNumberofdatasettrainingpoints...................................