MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution

Michael Faus; H. Vincent Poor; Alex Dytso

doi:10.1109/IEEECONF51394.2020.9443320

MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution

Michael Faus, H. Vincent Poor, Alex Dytso

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Abstract

This paper proposes new lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in a Kullback-Leibler divergence ball centered at some Gaussian distribution. The bounds are shown to hold for a larger family of distributions than the Cramér-Rao bound and are shown to be sharper than the Cramér-Rao bound in some regimes.

Original language	English (US)
Title of host publication	Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020
Editors	Michael B. Matthews
Publisher	IEEE Computer Society
Pages	1477-1478
Number of pages	2
ISBN (Electronic)	9780738131269
DOIs	https://doi.org/10.1109/IEEECONF51394.2020.9443320
State	Published - Nov 1 2020
Externally published	Yes
Event	54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020 - Pacific Grove, United States Duration: Nov 1 2020 → Nov 5 2020

Publication series

Name	Conference Record - Asilomar Conference on Signals, Systems and Computers
Volume	2020-November
ISSN (Print)	1058-6393

Conference

Conference	54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020
Country/Territory	United States
City	Pacific Grove
Period	11/1/20 → 11/5/20

All Science Journal Classification (ASJC) codes

Signal Processing
Computer Networks and Communications

Access to Document

10.1109/IEEECONF51394.2020.9443320

Cite this

Faus, M., Poor, H. V., & Dytso, A. (2020). MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution. In M. B. Matthews (Ed.), Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020 (pp. 1477-1478). Article 9443320 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2020-November). IEEE Computer Society. https://doi.org/10.1109/IEEECONF51394.2020.9443320

Faus, Michael ; Poor, H. Vincent ; Dytso, Alex. / MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution. Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020. editor / Michael B. Matthews. IEEE Computer Society, 2020. pp. 1477-1478 (Conference Record - Asilomar Conference on Signals, Systems and Computers).

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abstract = "This paper proposes new lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in a Kullback-Leibler divergence ball centered at some Gaussian distribution. The bounds are shown to hold for a larger family of distributions than the Cram{\'e}r-Rao bound and are shown to be sharper than the Cram{\'e}r-Rao bound in some regimes.",

author = "Michael Faus and Poor, {H. Vincent} and Alex Dytso",

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series = "Conference Record - Asilomar Conference on Signals, Systems and Computers",

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Faus, M, Poor, HV & Dytso, A 2020, MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution. in MB Matthews (ed.), Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020., 9443320, Conference Record - Asilomar Conference on Signals, Systems and Computers, vol. 2020-November, IEEE Computer Society, pp. 1477-1478, 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020, Pacific Grove, United States, 11/1/20. https://doi.org/10.1109/IEEECONF51394.2020.9443320

MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution. / Faus, Michael; Poor, H. Vincent; Dytso, Alex.
Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020. ed. / Michael B. Matthews. IEEE Computer Society, 2020. p. 1477-1478 9443320 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2020-November).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

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N2 - This paper proposes new lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in a Kullback-Leibler divergence ball centered at some Gaussian distribution. The bounds are shown to hold for a larger family of distributions than the Cramér-Rao bound and are shown to be sharper than the Cramér-Rao bound in some regimes.

AB - This paper proposes new lower and upper bounds on the minimum mean squared error (MMSE). The key idea is to minimize/maximize the MMSE subject to the constraint that the joint distribution of the input-output statistics lies in a Kullback-Leibler divergence ball centered at some Gaussian distribution. The bounds are shown to hold for a larger family of distributions than the Cramér-Rao bound and are shown to be sharper than the Cramér-Rao bound in some regimes.

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Faus M, Poor HV, Dytso A. MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution. In Matthews MB, editor, Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020. IEEE Computer Society. 2020. p. 1477-1478. 9443320. (Conference Record - Asilomar Conference on Signals, Systems and Computers). doi: 10.1109/IEEECONF51394.2020.9443320

MMSE Bounds under Kullback-Leibler Divergence Constraints on the Joint Input-Output Distribution

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