Greedy Learning of Binary Latent Trees二叉隐树的贪心学习

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1、1GreedyLearningofBinaryLatentTreesStefanHarmelingandChristopherK.I.WilliamsFAbstract—Inferringlatentstructuresfromobservationshelpstomodelvariablesareconditionallyindependentgiventhelatentandpossiblyalsounderstandunderlyingdatageneratingprocesses.Avariable2.Thismodelcanreadi

2、lybefittedtodatausingrichclassoflatentstructuresarethelatenttrees,i.e.tree-structuredtheEMalgorithm.However,ithasstrongassumptionsdistributionsinvolvinglatentvariableswherethevisiblevariablesareofconditionalindependencethatingeneralwillnotbeleaves.Thesearealsocalledhierarchic

3、allatentclass(HLC)models.justified.Zhang(2004)proposedasearchalgorithmforlearningsuchmodelsinthespiritofBayesiannetworkstructurelearning.WhilesuchanThesestrongassumptionscanberelaxedbyproposingapproachcanfindgoodsolutionsitcanbecomputationallyexpensive.aricher,tree-structuredl

4、atentvariablemodelaspro-Asanalternativeweinvestigatetwogreedyprocedures:theBIN-GposedforexampleinZhang(2004).FollowingZhangalgorithmdeterminesboththestructureofthetreeandthecardinalitywecallthisahierarchicallatentclass(HLC)model.Theofthelatentvariablesinabottom-upfashion.The

5、BIN-Aalgorithmfirstnetworkstructureisarootedtreeandtheleavesofthedeterminesthetreestructureusingagglomerativehierarchicalcluster-treearethevisiblevariables.Anattractionofalatenttreeing,andthendeterminesthecardinalityofthelatentvariablesasforstructure(comparedtomorecomplexDAGs

6、)isthatitBIN-G.WeshowthatevenwithrestrictingourselvestobinarytreesweobtainHLCmodelsofcomparablequalitytoZhang’ssolutions(inallowslineartimeinference(Pearl,1988).Furthermore,termsofcross-validatedlog-likelihood),whilebeinggenerallyfastertosuchalatentstructurereflectsahierarchi

7、calgroupingcompute.Thisclaimisvalidatedbyacomprehensivecomparisononofthevisiblevariables,makingHLCmodelsoftenin-severaldatasets.Furthermore,wedemonstratethatourmethodsareterpretableandgivinginsightsintothedatageneratingabletoestimateinterpretablelatentstructuresonreal-worldd

8、atawithprocesses.Weemphasizethedifferencebetweenthealargenumberofvariables.