Evaluation of error probability of classification based on the analysis of the bayes code

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

Suppose that we have two training sequences generated by parametrized distributions P θ 1∗ and P θ 2∗, where θ 1∗{\ast} and θ 2∗{\ast} are unknown. Given training sequences, we study the problem of classifying whether a test sequence was generated according to P θ 1∗ or P θ 2∗. This problem can be thought of as a hypothesis testing problem and the weighted sum of type-I and type-II error probabilities is analyzed. To prove the results, we utilize the analysis of the codeword lengths of the Bayes code. It is shown that upper and lower bounds of the probability of error are characterized by the terms containing the Chernoff information, the dimension of a parameter space, and the ratio of the length between the training sequences and the test sequence. Further, we generalize the part of the preceding results to multiple hypotheses setup.

Original languageEnglish
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages2510-2514
Number of pages5
ISBN (Electronic)9781728164328
DOIs
Publication statusPublished - 2020 Jun
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: 2020 Jul 212020 Jul 26

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2020-June
ISSN (Print)2157-8095

Conference

Conference2020 IEEE International Symposium on Information Theory, ISIT 2020
CountryUnited States
CityLos Angeles
Period20/7/2120/7/26

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Information Systems
  • Modelling and Simulation
  • Applied Mathematics

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