2026-09-20T03:45:38Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/447172022-01-13T07:54:29Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Silvio Micali.
Valiant, Paul (Paul Andrew)
Massachusetts Institute of Technology. Dept. of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2009-03-16T19:33:34Z
2009-03-16T19:33:34Z
2008
2008
http://hdl.handle.net/1721.1/44717
297547243
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.
Includes bibliographical references (p. 65-66).
We introduce the notion of a Canonical Tester for a class of properties on distributions, that is, a tester strong and general enough that "a distribution property in the class is testable if and only if the Canonical Tester tests it". We construct a Canonical Tester for the class of symmetric properties of one or two distributions, satisfying a certain weak continuity condition. Analyzing the performance of the Canonical Tester on specific properties resolves several open problems, establishing lower bounds that match known upper bounds: we show that distinguishing between entropy < a or > p on distributions over [n] requires nc/P-O(1) samples, and distinguishing whether a pair of distributions has statistical distance < a or > 0 requires n1-o(1) samples. Our techniques also resolve a conjecture about a property that our Canonical Tester does not apply to: distinguishing identical distributions from those with statistical distance > 0 requires Q(n2/3) samples.
by Paul Valiant.
Ph.D.
66 p.
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by
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http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Testing symmetric properties of distributions
Thesis
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Publication
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<Abstract>We introduce the notion of a Canonical Tester for a class of properties on distributions, that is, a tester strong and general enough that "a distribution property in the class is testable if and only if the Canonical Tester tests it". We construct a Canonical Tester for the class of symmetric properties of one or two distributions, satisfying a certain weak continuity condition. Analyzing the performance of the Canonical Tester on specific properties resolves several open problems, establishing lower bounds that match known upper bounds: we show that distinguishing between entropy < a or > p on distributions over [n] requires nc/P-O(1) samples, and distinguishing whether a pair of distributions has statistical distance < a or > 0 requires n1-o(1) samples. Our techniques also resolve a conjecture about a property that our Canonical Tester does not apply to: distinguishing identical distributions from those with statistical distance > 0 requires Q(n2/3) samples.</Abstract>
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