A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications

Alex Dytso, H. Vincent Poor, Shlomo Shamai Shitz

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

Abstract

This paper provides a general derivative identity for the conditional mean estimator of an arbitrary vector signal in Gaussian noise with an arbitrary covariance matrix. This new identity is used to recover and generalize many known identities in the literature and derive some new identities. For example, a new identity is discovered, which shows that an arbitrary higher-order conditional moment is completely determined by the first conditional moment.Several applications of the identities are shown. For instance, by using one of the identities, a simple proof of the uniqueness of the conditional mean estimator as a function of the distribution of the signal is shown. Moreover, one of the identities is used to extend the notion of empirical Bayes to higher-order conditional moments. Specifically, based on a random sample of noisy observations, a consistent estimator for a conditional expectation of any order is derived.

Original languageEnglish (US)
Title of host publication2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages1183-1188
Number of pages6
ISBN (Electronic)9781728164328
DOIs
StatePublished - Jun 2020
Event2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States
Duration: Jul 21 2020Jul 26 2020

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
Period7/21/207/26/20

All Science Journal Classification (ASJC) codes

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

Keywords

  • Conditional mean estimator
  • empirical Bayes
  • Gaussian Noise

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  • Cite this

    Dytso, A., Poor, H. V., & Shamai Shitz, S. (2020). A General Derivative Identity for the Conditional Mean Estimator in Gaussian Noise and Some Applications. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 1183-1188). [9174071] (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT44484.2020.9174071