Title

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.

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

Share

 
COinS