Error Exponents in Distributed Hypothesis Testing of Correlations

Uri Hadar; Jingbo Liu; Yury Polyanskiy; Ofer Shayevitz

doi:https://doi.org/10.1109/ISIT.2019.8849426

Error Exponents in Distributed Hypothesis Testing of Correlations

Uri Hadar, Jingbo Liu, Yury Polyanskiy, Ofer Shayevitz

School of Electrical Engineering

Tel Aviv University

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

Abstract

We study a distributed hypothesis testing problem where two parties observe i.i.d. samples from two ρ-correlated standard normal random variables X and Y. The party that observes the X-samples can communicate R bits per sample to the second party, that observes the Y-samples, in order to test between two correlation values. We investigate the best possible type-II error subject to a fixed type-I error, and derive an upper (impossibility) bound on the associated type-II error exponent. Our techniques include representing the conditional Y-samples as a trajectory of the Ornstein-Uhlenbeck process, and bounding the associated KL divergence using the subadditivity of the Wasserstein distance and the Gaussian Talagrand inequality.

Original language	English
Title of host publication	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	2674-2678
Number of pages	5
ISBN (Electronic)	9781538692912
DOIs	https://doi.org/10.1109/ISIT.2019.8849426
State	Published - Jul 2019
Event	2019 IEEE International Symposium on Information Theory, ISIT 2019 - Paris, France Duration: 7 Jul 2019 → 12 Jul 2019

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2019-July

Conference

Conference	2019 IEEE International Symposium on Information Theory, ISIT 2019
Country/Territory	France
City	Paris
Period	7/07/19 → 12/07/19

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Information Systems
Modelling and Simulation
Applied Mathematics

Access to Document

https://doi.org/10.1109/ISIT.2019.8849426

Cite this

Hadar, U., Liu, J., Polyanskiy, Y., & Shayevitz, O. (2019). Error Exponents in Distributed Hypothesis Testing of Correlations. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings (pp. 2674-2678). Article 8849426 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT.2019.8849426

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author = "Uri Hadar and Jingbo Liu and Yury Polyanskiy and Ofer Shayevitz",

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Hadar, U, Liu, J, Polyanskiy, Y & Shayevitz, O 2019, Error Exponents in Distributed Hypothesis Testing of Correlations. in 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings., 8849426, IEEE International Symposium on Information Theory - Proceedings, vol. 2019-July, Institute of Electrical and Electronics Engineers Inc., pp. 2674-2678, 2019 IEEE International Symposium on Information Theory, ISIT 2019, Paris, France, 7/07/19. https://doi.org/10.1109/ISIT.2019.8849426

Error Exponents in Distributed Hypothesis Testing of Correlations. / Hadar, Uri; Liu, Jingbo; Polyanskiy, Yury et al.
2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2019. p. 2674-2678 8849426 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2019-July).

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

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AB - We study a distributed hypothesis testing problem where two parties observe i.i.d. samples from two ρ-correlated standard normal random variables X and Y. The party that observes the X-samples can communicate R bits per sample to the second party, that observes the Y-samples, in order to test between two correlation values. We investigate the best possible type-II error subject to a fixed type-I error, and derive an upper (impossibility) bound on the associated type-II error exponent. Our techniques include representing the conditional Y-samples as a trajectory of the Ornstein-Uhlenbeck process, and bounding the associated KL divergence using the subadditivity of the Wasserstein distance and the Gaussian Talagrand inequality.

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Hadar U, Liu J, Polyanskiy Y, Shayevitz O. Error Exponents in Distributed Hypothesis Testing of Correlations. In 2019 IEEE International Symposium on Information Theory, ISIT 2019 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2019. p. 2674-2678. 8849426. (IEEE International Symposium on Information Theory - Proceedings). doi: https://doi.org/10.1109/ISIT.2019.8849426

Error Exponents in Distributed Hypothesis Testing of Correlations

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All Science Journal Classification (ASJC) codes

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