bayesian reasoning and machine learning

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

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

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

4、lesXareindependentofvariablesYconditionedonvariablesZ.11X>>YjZVariablesXaredependentonvariablesYconditionedonvariablesZ..11RRForcontinuousvariablesthisisshorthandforf(x)dxandfordiscretevari-f(x)Pxablesmeanssummationoverthestatesofx,f(x)..................17

5、xI[S]Indicator:hasvalue1ifthestatementSistrue,0otherwise..........19pa(x)Theparentsofnodex.................................................26ch(x)Thechildrenofnodex.................................................26ne(x)Neighboursofnodex...................

6、...............................26dim(x)Foradiscretevariablex,thisdenotesthenumberofstatesxcantake..34hf(x)iTheaverageofthefunctionf(x)withrespecttothedistributionp(x).158p(x)Deltafunction.Fordiscretea,b,thisistheKroneckerdelta,a;bandfor(a;b)continuousa,b

7、theDiracdeltafunction(ab)......................160dimxThedimensionofthevector/matrixx................................171](x=s;y=t)Thenumberoftimesxisinstatesandyinstatetsimultaneously...195]xyThenumberoftimesvariablexisinstatey..........................2

8、76DDataset...............................................................289nDataindex...........................................................289NNumberofdatasettrainingpoints..............................