marginal independence

《marginal independence》由会员上传分享，免费在线阅读，更多相关内容在教育资源-天天文库。

1、MarginalIndependenceandConditionalIndependenceComputerSciencecpsc322,Lecture26(TextbookChpt6.1-2)March,19,2010LectureOverview•RecapwithExample–Marginalization–ConditionalProbability–ChainRule•Bayes'Rule•MarginalIndependence•ConditionalIndependenceourmostbasicandrobustformofknowledgeabou

2、tuncertainenvironments.RecapJointDistribution•3binaryrandomvariables:P(H,S,F)–Hdom(H)={h,h}hasheartdisease,doesnothave…–Sdom(S)={s,s}smokes,doesnotsmoke–Fdom(F)={f,f}highfatdiet,lowfatdietRecapJointDistribution•3binaryrandomvariables:P(H,S,F)–Hdom(H)={h,h}hasheartdisease,doesnothave

3、…–Sdom(S)={s,s}smokes,doesnotsmoke–Fdom(F)={f,f}highfatdiet,lowfatdietffssssh.015.007.005.003h.21.51.07.18RecapMarginalizationffssssh.015.007.005.003h.21.51.07.18P(H,S)P(H,S,Fx)xdom(F)P(H,S)?.02.01P(H)?.28.69P(S)?RecapConditionalProbabilityP(H,S)ssP(H)P(S,H)P(S

4、H)h.02.01

5、.03P(H)h.28.69.97P(S).30.70P(S

6、H)ssP(H

7、S)h.666.333h.29.71RecapConditionalProbability(cont.)P(S,H)P(S

8、H)P(H)Twokeypointswecoveredinpreviouslecture•Wederivedthisequalityfromapossibleworldsemanticsofprobability•Itisnotaprobabilitydistributionsbut…..•Oneforeachconfigurationoftheconditio

9、ningvar(s)RecapChainRuleP(H,S,F)BayesTheoremP(S,H)P(S,H)P(S

10、H)P(H

11、S)P(H)P(S)P(H

12、S)P(S)P(S

13、H)P(H)LectureOverview•RecapwithExampleandBayesTheorem•MarginalIndependence•ConditionalIndependenceDoyoualwaysneedtoreviseyourbeliefs?……whenyourknowledgeofY’svaluedoesn’taffectyourbeliefintheval

14、ueofXDEF.RandomvariableXismarginalindependentofrandomvariableYif,forallxdom(X),ydom(Y),ikP(X=x

15、Y=y)=P(X=x)ikiMarginalIndependence:Example•XandYareindependentiff:P(X

16、Y)=P(X)orP(Y

17、X)=P(Y)orP(X,Y)=P(X)P(Y)•ThatisnewevidenceY(orX)doesnotaffectcurrentbeliefinX(orY)•Ex:P(Toothache,Catch,Cav

18、ity,Weather)=P(Toothache,Catch,Cavity.•JPDrequiringentriesisreducedtotwosmallerones(and)InourexampleareSmokingandHeartDiseasemarginallyIndependent?Whatourprobabilitiesaretellingus….?P(H,S)ssP(H)h.02.01.03h.28.69.97P(S).30.70P(S

19、H)ssh.666.334h.29.71LectureOverview•RecapwithE