2026-09-18T18:39:51Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/998642022-01-13T07:54:01Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
Ronitt Rubinfeld.
Gouleakis, Themistoklis
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2015-11-09T19:53:56Z
2015-11-09T19:53:56Z
2015
2015
http://hdl.handle.net/1721.1/99864
928001806
Thesis: S.M., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.
Title as it appears in MIT Commencement Exercises program, June 5, 2015: Testing and correcting probability distributions. Cataloged from PDF version of thesis.
Includes bibliographical references (pages 61-63).
We study the question of testing structured properties of discrete distributions. Specifically, given sample access to an arbitrary distribution D over [n] and a property P, the goal is to distinguish between ... Building on a result of [9], we develop a general algorithm for this question, which applies to a large range of "shape-constrained" properties, including monotone, log-concave, t-modal and Poisson Binomial distributions. Our generic property tester works for properties that exclusively contain distributions which can be well approximated by L-histograms for a small (usually logarithmic in the domain size) value of L. The sample complexity of this generic approach is ... Moreover, for all cases considered, our algorithm has near-optimal sample complexity. Finally, we also describe a generic method to prove lower bounds for this problem, and use it to derive strong converses to our algorithmic results. More specifically, we use the following reduction technique: we compose the property tester for a class-C of distributions with an agnostic learner for that same class to get a tester for subset CHARD ... C for which a lower bound is known.
by Themistoklis Gouleakis.
S.M.
63 pages
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Testing shape restriction properties of probability distributions in a unified way
Testing and correcting probability distributions
Thesis
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