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dc.contributor.advisorCaroline Uhler.en_US
dc.contributor.authorSaeed, Basil(Basil N.)en_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2020-09-15T22:01:46Z
dc.date.available2020-09-15T22:01:46Z
dc.date.copyright2020en_US
dc.date.issued2020en_US
dc.identifier.urihttps://hdl.handle.net/1721.1/127515
dc.descriptionThesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, May, 2020en_US
dc.descriptionCataloged from the official PDF of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 55-56).en_US
dc.description.abstractWe consider the problem of learning directed graphical models with latent variables, represented by directed maximal ancestral graphs, from a conditional independence oracle. We show that given a set of separation statements from some directed maximal ancestral graph G* = (V*,E*), we can map posets with ground set V* to minimal IMAPs of G* such that the sparsest of these minimal IMAPs is Markov equivalent to G*. We give a diagrammatic interpretation of these minimal IMAPs in terms of the Hasse diagram of the poset of posets. Namely, the Hasse diagram of these minimal IMAPs corresponds to the Hasse diagram of the poset of posets after identifying posets that map to the same minimal IMAP. We show that moving between these minimal IMAPs using legitimate mark changes corresponds to covering relations in the poset obtained after identification. Finally, we conjecture that a greedy search to minimize sparsity over this contracted space by moving between minimal IMAPs using legitimate mark changes converges to G*.en_US
dc.description.statementofresponsibilityby Basil Saeed.en_US
dc.format.extent56 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT theses may be protected by copyright. Please reuse MIT thesis content according to the MIT Libraries Permissions Policy, which is available through the URL provided.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleLearning directed graphical models with latent variablesen_US
dc.typeThesisen_US
dc.description.degreeM. Eng.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Scienceen_US
dc.identifier.oclc1193029183en_US
dc.description.collectionM.Eng. Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Scienceen_US
dspace.imported2020-09-15T22:01:46Zen_US
mit.thesis.degreeMasteren_US
mit.thesis.departmentEECSen_US


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