bayesian reasoning and machine learning

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1、BayesianReasoningandMachineLearningDavidBarberc2007,2008,2009,2010,2011,2012,2013NotationListVacalligraphicsymboltypicallydenotesasetofrandomvariables........7dom(x)Domainofavariable....................................................7x=xThevariablexisinthestatex........................

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

3、................................8p(x[y)probabilityofxory....................................................8p(xjy)Theprobabilityofxconditionedony...................................8X??YjZVariablesXareindependentofvariablesYconditionedonvariablesZ.11X>>YjZVariablesXaredependentonvariabl

4、esYconditionedonvariablesZ..11RRForcontinuousvariablesthisisshorthandforf(x)dxandfordiscretevari-f(x)Pxablesmeanssummationoverthestatesofx,f(x)..................17xI[S]Indicator:hasvalue1ifthestatementSistrue,0otherwise..........19pa(x)Theparentsofnodex..................................

5、...............26ch(x)Thechildrenofnodex.................................................26ne(x)Neighboursofnodex..................................................26dim(x)Foradiscretevariablex,thisdenotesthenumberofstatesxcantake..34hf(x)iTheaverageofthefunctionf(x)withrespecttothedistr

6、ibutionp(x).158p(x)Deltafunction.Fordiscretea,b,thisistheKroneckerdelta,a;bandfor(a;b)continuousa,btheDiracdeltafunction(ab)......................160dimxThedimensionofthevector/matrixx................................171](x=s;y=t)Thenumberoftimesxisinstatesandyinstatetsimultaneously.

7、..195]xyThenumberoftimesvariablexisinstatey..........................276DDataset...............................................................289nDataindex...........................................................289NNumberofdatasettrainingpoints..............................