On MDL Estimation for Simple Contaminated Gaussian Location Families

Kohei Miyamoto, Jun'Ichi Takeuchi

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

Abstract

The performance of MDL density estimators defined as the minimizer of two part code lengths isguaranteed in terms of the redundancy of the two part code [2], [3]. When the true density belongs to the assumed model, the redundancy of a code can be bounded by the regret (pointwise redundancy) of the code. Then, the construction of two part codes which achieve small regret based on quantization of parametric family is developed. For exponential families, it is known that we can achieve sufficiently small regret by using this construction [4]. For non-exponential families, the evaluation of the regret achieved by using this construction breaks. However, for non-exponential families under certain assumptions, by enhancing this construction using local exponentially family bundles [1], we can design efficient two part codes [9]. In this paper, we show that we can apply this coding method to contamination model [5] with simple settings and give the guarantee of performance of MDL estimators for them.

Original languageEnglish
Title of host publicationProceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages587-591
Number of pages5
ISBN (Electronic)9784885523304
Publication statusPublished - Oct 24 2020
Event16th International Symposium on Information Theory and its Applications, ISITA 2020 - Virtual, Kapolei, United States
Duration: Oct 24 2020Oct 27 2020

Publication series

NameProceedings of 2020 International Symposium on Information Theory and its Applications, ISITA 2020

Conference

Conference16th International Symposium on Information Theory and its Applications, ISITA 2020
CountryUnited States
CityVirtual, Kapolei
Period10/24/2010/27/20

All Science Journal Classification (ASJC) codes

  • Computational Theory and Mathematics
  • Computer Science Applications
  • Information Systems
  • Software
  • Theoretical Computer Science

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