Testing shape restriction properties of probability distributions in a unified way
Name
928001806-MIT.pdf
Description
Full printable version
Size
2.49 MB
Format
Adobe PDF
Checksum (MD5)
2e93f337173350f2e676c5886f3ebcd9
Author(s)
Gouleakis, Themistoklis
Advisor(s)
Ronitt Rubinfeld.
Alternative Title
Testing and correcting probability distributions
Date Issued
2015
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
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).
Subjects
Electrical Engineering and Computer Science.
MIT Department
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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