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Article
Optimal Confidence Sets for the Multinomial Parameter
Proceedings of the IEEE International Symposium on Information Theory (2021, Melbourne, Australia)
  • Matthew L. Malloy
  • Ardhendu S. Tripathy, Missouri University of Science and Technology
  • Robert D. Nowak
Abstract

Construction of tight confidence sets and intervals is central to statistical inference and decision making. This paper develops new theory showing minimum average volume confidence sets for categorical data. More precisely, consider an empirical distribution p̂ generated from n iid realizations of a random variable that takes one of k possible values according to an unknown distribution p. This is analogous to a single draw from a multinomial distribution. A confidence set is a subset of the probability simplex that depends on p̂ and contains the unknown p with a specified confidence. This paper shows how one can construct minimum average volume confidence sets. The optimality of the sets translates to improved sample complexity for adaptive machine learning algorithms that rely on confidence sets, regions and intervals.

Meeting Name
2021 IEEE International Symposium on Information Theory, ISIT (2021: Jul. 12-20, Melbourne, Australia)
Department(s)
Computer Science
International Standard Book Number (ISBN)
978-153868209-8
Document Type
Article - Conference proceedings
Document Version
Citation
File Type
text
Language(s)
English
Rights
© 2021 Institute of Electrical and Electronics Engineers (IEEE), All rights reserved.
Publication Date
7-20-2021
Publication Date
20 Jul 2021
Disciplines
Citation Information
Matthew L. Malloy, Ardhendu S. Tripathy and Robert D. Nowak. "Optimal Confidence Sets for the Multinomial Parameter" Proceedings of the IEEE International Symposium on Information Theory (2021, Melbourne, Australia) (2021) p. 2173 - 2178 ISSN: 2157-8095
Available at: http://works.bepress.com/ardhendu-s-tripathy/16/