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dc.contributor.advisorGregory Wornell.en_US
dc.contributor.authorAjjanagadde, Ganeshen_US
dc.contributor.otherMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.en_US
dc.date.accessioned2017-12-20T17:23:55Z
dc.date.available2017-12-20T17:23:55Z
dc.date.copyright2016en_US
dc.date.issued2016en_US
dc.identifier.urihttp://hdl.handle.net/1721.1/112818
dc.descriptionThesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2016.en_US
dc.descriptionThis electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.en_US
dc.descriptionCataloged from student-submitted PDF version of thesis.en_US
dc.descriptionIncludes bibliographical references (pages 51-53).en_US
dc.description.abstractThis thesis explores the problems of learning analysis of variance (ANOVA) decompositions over GF(2) and R, as well as a general regression setup. For the problem of learning ANOVA decompositions, we obtain fundamental limits in the case of GF(2) under both sparsity and degree structures. We show how the degree or sparsity level is a useful measure of the complexity of such models, and in particular how the statistical complexity ranges from linear to exponential in the dimension, thus forming a "learning hierarchy". Furthermore, we discuss the problem in both an "adaptive" as well as a "one-shot" setting, where in the adaptive case query choice can depend on the entire past history. Somewhat surprisingly, we show that the "adaptive" setting does not yield significant statistical gains. In the case of R, under query access, we demonstrate an approach that achieves a similar hierarchy of complexity with respect to the dimension. For the general regression setting, we outline a viewpoint that captures a variety of popular methods based on locality and partitioning of some kind. We demonstrate how "data independent" partitioning may still yield statistically consistent estimators, and illustrate this by a lattice based partitioning approach.en_US
dc.description.statementofresponsibilityby Ganesh Ajjanagadde.en_US
dc.format.extent53 pagesen_US
dc.language.isoengen_US
dc.publisherMassachusetts Institute of Technologyen_US
dc.rightsMIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.en_US
dc.rights.urihttp://dspace.mit.edu/handle/1721.1/7582en_US
dc.subjectElectrical Engineering and Computer Science.en_US
dc.titleA learning hierarchy for classification and regressionen_US
dc.typeThesisen_US
dc.description.degreeM. Eng.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
dc.identifier.oclc1014171329en_US


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