Modern challenges in distribution testing
Name
1084273332-MIT.pdf
Description
Full printable version
Size
6.57 MB
Format
Adobe PDF
Checksum (MD5)
ba633f5811b5d6f72617ed6f9ab05cb7
Author(s)
Kamath, Gautam (Gautam Chetan)
Advisor(s)
Constantinos Daskalakis.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
Hypothesis testing is one of the most classical problems in statistics. While it has enjoyed over a century of intense study, only recent focus has been on the small-sample regime, with interest in sample complexities and minimax rates. Our understanding of many fundamental problems is now quite mature, but there are several questions which have arisen over the last decade, which have not yet received adequate attention. The goal of this dissertation is to identify and address several contemporary challenges in distribution testing. In particular, we make progress in answering the following questions: ** Can we test distributions with tolerance to model misspecification? ** How does the complexity of distribution testing change as we consider different measures of distance? ** Can we efficiently test for membership in (potentially infinite) classes of distributions? ** How can we avoid the curse of dimensionality when testing multivariate distributions? ** Is it possible to perform hypothesis testing on sensitive data, while respecting privacy of the dataset? ** Can we design more efficient algorithms if the dataset is sampled actively? Directions for further investigation are also discussed.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2018.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 321-356).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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