MIT Libraries logoDSpace@MIT

MIT
View Item 
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Graduate Theses
  • View Item
  • DSpace@MIT Home
  • MIT Libraries
  • MIT Theses
  • Graduate Theses
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Learning directed graphical models with latent variables

Author(s)
Saeed, Basil(Basil N.)
Thumbnail
Download1193029183-MIT.pdf (2.018Mb)
Other Contributors
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Advisor
Caroline Uhler.
Terms of use
MIT 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. http://dspace.mit.edu/handle/1721.1/7582
Metadata
Show full item record
Abstract
We 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*.
Description
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, May, 2020
 
Cataloged from the official PDF of thesis.
 
Includes bibliographical references (pages 55-56).
 
Date issued
2020
URI
https://hdl.handle.net/1721.1/127515
Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
Publisher
Massachusetts Institute of Technology
Keywords
Electrical Engineering and Computer Science.

Collections
  • Graduate Theses

Browse

All of DSpaceCommunities & CollectionsBy Issue DateAuthorsTitlesSubjectsThis CollectionBy Issue DateAuthorsTitlesSubjects

My Account

Login

Statistics

OA StatisticsStatistics by CountryStatistics by Department
MIT Libraries
PrivacyPermissionsAccessibilityContact us
MIT
Content created by the MIT Libraries, CC BY-NC unless otherwise noted. Notify us about copyright concerns.