Recovering Structure of Noisy Data through Hypothesis Testing

Minoh Jeong; Alex Dytso; Martina Cardone; H. Vincent Poor

doi:10.1109/ISIT44484.2020.9174229

Recovering Structure of Noisy Data through Hypothesis Testing

Minoh Jeong, Alex Dytso, Martina Cardone, H. Vincent Poor

Electrical and Computer Engineering

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

4 Scopus citations

Abstract

This paper considers a noisy data structure recovery problem. Specifically, the goal is to investigate the following question: Given a noisy observation of the data, according to which permutation was the original data sorted? The main focus is on scenarios where data is generated according to an isotropic Gaussian distribution, and the perturbation consists of adding Gaussian noise with diagonal scalar covariance matrix. This problem is posed within a hypothesis testing framework. First, the optimal decision criterion is characterized and shown to be identical to the hypothesis of the observation. Then, by leveraging the structure of the optimal decision criterion, the probability of error is characterized. Finally, the logarithmic behavior (i.e., the exponent) of the probability of error is derived in the regime where the dimension of the data goes to infinity.

Original language	English (US)
Title of host publication	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1307-1312
Number of pages	6
ISBN (Electronic)	9781728164328
DOIs	https://doi.org/10.1109/ISIT44484.2020.9174229
State	Published - Jun 2020
Event	2020 IEEE International Symposium on Information Theory, ISIT 2020 - Los Angeles, United States Duration: Jul 21 2020 → Jul 26 2020

Publication series

Name	IEEE International Symposium on Information Theory - Proceedings
Volume	2020-June
ISSN (Print)	2157-8095

Conference

Conference	2020 IEEE International Symposium on Information Theory, ISIT 2020
Country/Territory	United States
City	Los Angeles
Period	7/21/20 → 7/26/20

Bibliographical note

Funding Information:
The work of M. Jeong and M. Cardone was supported in part by the U.S. National Science Foundation under Grant CCF-1849757. The work of A. Dytso and H. V. Poor was supported in part by the U.S. National Science Foundation under Grant CCF-1908308

Publisher Copyright:
© 2020 IEEE.

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Jeong, M., Dytso, A., Cardone, M., & Poor, H. V. (2020). Recovering Structure of Noisy Data through Hypothesis Testing. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings (pp. 1307-1312). Article 9174229 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ISIT44484.2020.9174229

Recovering Structure of Noisy Data through Hypothesis Testing. / Jeong, Minoh; Dytso, Alex; Cardone, Martina et al.
2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc., 2020. p. 1307-1312 9174229 (IEEE International Symposium on Information Theory - Proceedings; Vol. 2020-June).

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

Jeong, M, Dytso, A, Cardone, M & Poor, HV 2020, Recovering Structure of Noisy Data through Hypothesis Testing. in 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings., 9174229, IEEE International Symposium on Information Theory - Proceedings, vol. 2020-June, Institute of Electrical and Electronics Engineers Inc., pp. 1307-1312, 2020 IEEE International Symposium on Information Theory, ISIT 2020, Los Angeles, United States, 7/21/20. https://doi.org/10.1109/ISIT44484.2020.9174229

Jeong M, Dytso A, Cardone M, Poor HV. Recovering Structure of Noisy Data through Hypothesis Testing. In 2020 IEEE International Symposium on Information Theory, ISIT 2020 - Proceedings. Institute of Electrical and Electronics Engineers Inc. 2020. p. 1307-1312. 9174229. (IEEE International Symposium on Information Theory - Proceedings). doi: 10.1109/ISIT44484.2020.9174229

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Recovering Structure of Noisy Data through Hypothesis Testing

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