Optimal Confidence Sets for the Multinomial Parameter
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.
Recommended Citation
M. L. Malloy et al., "Optimal Confidence Sets for the Multinomial Parameter," Proceedings of the IEEE International Symposium on Information Theory (2021, Melbourne, Australia), pp. 2173 - 2178, Institute of Electrical and Electronics Engineers (IEEE), Jul 2021.
The definitive version is available at https://doi.org/10.1109/ISIT45174.2021.9517964
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
International Standard Serial Number (ISSN)
2157-8095
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
20 Jul 2021
