Learning continuous sparse pairwise Markov random fields
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1252064284-MIT.pdf
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462.64 KB
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Author(s)
Shah, Abhin Swapnil.
Advisor(s)
Devavrat Shah and Gregory W. Wornell.
Date Issued
2021
Publisher
Massachusetts Institute of Technology
Abstract
We consider learning a sparse pairwise Markov Random Field with continuous valued variables from i.i.d samples. We adapt the framework of generalized interaction screening objective to this setting and provide finite-sample analysis revealing sample complexity scaling logarithmically with the number of variables, as in the discrete and Gaussian settings. Our approach is applicable to a large class of pairwise Markov Random Fields with continuous variables and also has desirable asymptotic properties, including consistency and normality under mild conditions. Further, we establish that the population version of generalized interaction screening objective can be interpreted as local maximum likelihood estimation. As part of our analysis, we introduce a robust variation of sparse linear regression à la Lasso, which may be of interest in its own right.
Description
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, February, 2021
Cataloged from the official PDF version of thesis.
Includes bibliographical references (pages 123-128).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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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.
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