Monotonicity of the Trace-Inverse of Covariance Submatrices and Two-Sided Prediction

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

It is common to assess the "memory strength"of a stationary process by looking at how fast the normalized log- determinant of its covariance submatrices (i.e., entropy rate) decreases. In this work, we propose an alternative characterization in terms of the normalized trace-inverse of the covariance submatrices. We show that this sequence is monotonically non-decreasing and is constant if and only if the process is white. Furthermore, while the entropy rate is associated with one-sided prediction errors (present from past), the new measure is associated with two-sided prediction errors (present from past and future). Minimizing this measure is then used as an alternative to Burg's maximum-entropy principle for spectral estimation.

Original languageEnglish
Title of host publication2022 IEEE International Symposium on Information Theory, ISIT 2022
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages450-455
Number of pages6
ISBN (Electronic)9781665421591
DOIs
StatePublished - 2022
Event2022 IEEE International Symposium on Information Theory, ISIT 2022 - Espoo, Finland
Duration: 26 Jun 20221 Jul 2022

Publication series

NameIEEE International Symposium on Information Theory - Proceedings
Volume2022-June
ISSN (Print)2157-8095

Conference

Conference2022 IEEE International Symposium on Information Theory, ISIT 2022
Country/TerritoryFinland
CityEspoo
Period26/06/221/07/22

Funding

FundersFunder number
Israel Ministry of Economy and Industry
Israel Science Foundation2427/19, 2623/20, 2077/20

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