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Entropy 2017, 19(7), 315; doi:10.3390/e19070315

The Expected Missing Mass under an Entropy Constraint

1
Department of Mathematics, Ben-Gurion University, Beer Sheva 84105, Israel
2
Department of Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel
*
Author to whom correspondence should be addressed.
Received: 7 June 2017 / Revised: 20 June 2017 / Accepted: 26 June 2017 / Published: 29 June 2017
(This article belongs to the Special Issue Information Theory in Machine Learning and Data Science)
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Abstract

In Berend and Kontorovich (2012), the following problem was studied: A random sample of size t is taken from a world (i.e., probability space) of size n; bound the expected value of the probability of the set of elements not appearing in the sample (unseen mass) in terms of t and n. Here we study the same problem, where the world may be countably infinite, and the probability measure on it is restricted to have an entropy of at most h. We provide tight bounds on the maximum of the expected unseen mass, along with a characterization of the measures attaining this maximum. View Full-Text
Keywords: missing mass; probability estimate; sampling; entropy missing mass; probability estimate; sampling; entropy
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Berend, D.; Kontorovich, A.; Zagdanski, G. The Expected Missing Mass under an Entropy Constraint. Entropy 2017, 19, 315.

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