On likelihood functions to minimize KL divergence in binary hypothesis testing

Linlin Sun; Shihao Yan; Riqing Chen; Feng Shu

doi:10.1109/ICSPCS50536.2020.9310022

On likelihood functions to minimize KL divergence in binary hypothesis testing

Linlin Sun, Shihao Yan, Riqing Chen, Feng Shu

School of Engineering

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

1 Citation (Scopus)

Abstract

Kullback-Leibler (KL) divergence is widely used to determine lower bounds on detection error probability for binary hypothesis testing in covert communications and location verification systems. For a Gaussian likelihood function under the null hypothesis H ₀ , it has been proved that it is a Gaussian likelihood function under the alternative hypothesis H ₁ that minimizes the KL divergence from H ₁ to H ₀ . Due to the asymmetry of KL divergence, it is still unclear what is the optimal likelihood function under H ₁ that minimizes the KL divergence from H ₀ to H ₁ . Surprisingly, in this work we prove that this optimal likelihood function is unachievable.

Original language	English
Title of host publication	2020, 14th International Conference on Signal Processing and Communication Systems, (ICSPCS)
Subtitle of host publication	proceedings
Editors	Tadeusz A. Wysocki, Beata J. Wysocki
Place of Publication	Piscataway, NJ
Publisher	Institute of Electrical and Electronics Engineers (IEEE)
Number of pages	5
ISBN (Electronic)	9781728199726, 9781728199719
ISBN (Print)	9781728199719
DOIs	https://doi.org/10.1109/ICSPCS50536.2020.9310022
Publication status	Published - 2020
Event	14th International Conference on Signal Processing and Communication Systems, ICSPCS 2020 - Virtual, Adelaide, Australia Duration: 14 Dec 2020 → 16 Dec 2020

Conference

Conference	14th International Conference on Signal Processing and Communication Systems, ICSPCS 2020
Country/Territory	Australia
City	Virtual, Adelaide
Period	14/12/20 → 16/12/20

Access to Document

10.1109/ICSPCS50536.2020.9310022

Cite this

Sun, L., Yan, S., Chen, R., & Shu, F. (2020). On likelihood functions to minimize KL divergence in binary hypothesis testing. In T. A. Wysocki, & B. J. Wysocki (Eds.), 2020, 14th International Conference on Signal Processing and Communication Systems, (ICSPCS): proceedings Institute of Electrical and Electronics Engineers (IEEE). https://doi.org/10.1109/ICSPCS50536.2020.9310022

@inproceedings{632b2b204f0a4df98fbff346bf7ae7ef,

title = "On likelihood functions to minimize KL divergence in binary hypothesis testing",

abstract = "Kullback-Leibler (KL) divergence is widely used to determine lower bounds on detection error probability for binary hypothesis testing in covert communications and location verification systems. For a Gaussian likelihood function under the null hypothesis H 0 , it has been proved that it is a Gaussian likelihood function under the alternative hypothesis H 1 that minimizes the KL divergence from H 1 to H 0 . Due to the asymmetry of KL divergence, it is still unclear what is the optimal likelihood function under H 1 that minimizes the KL divergence from H 0 to H 1 . Surprisingly, in this work we prove that this optimal likelihood function is unachievable.",

author = "Linlin Sun and Shihao Yan and Riqing Chen and Feng Shu",

year = "2020",

doi = "10.1109/ICSPCS50536.2020.9310022",

language = "English",

isbn = "9781728199719",

editor = "Wysocki, \{Tadeusz A.\} and Wysocki, \{Beata J.\}",

booktitle = "2020, 14th International Conference on Signal Processing and Communication Systems, (ICSPCS)",

publisher = "Institute of Electrical and Electronics Engineers (IEEE)",

address = "United States",

note = "14th International Conference on Signal Processing and Communication Systems, ICSPCS 2020 ; Conference date: 14-12-2020 Through 16-12-2020",

}

Sun, L, Yan, S, Chen, R & Shu, F 2020, On likelihood functions to minimize KL divergence in binary hypothesis testing. in TA Wysocki & BJ Wysocki (eds), 2020, 14th International Conference on Signal Processing and Communication Systems, (ICSPCS): proceedings. Institute of Electrical and Electronics Engineers (IEEE), Piscataway, NJ, 14th International Conference on Signal Processing and Communication Systems, ICSPCS 2020, Virtual, Adelaide, Australia, 14/12/20. https://doi.org/10.1109/ICSPCS50536.2020.9310022

On likelihood functions to minimize KL divergence in binary hypothesis testing. / Sun, Linlin; Yan, Shihao; Chen, Riqing et al.
2020, 14th International Conference on Signal Processing and Communication Systems, (ICSPCS): proceedings. ed. / Tadeusz A. Wysocki; Beata J. Wysocki. Piscataway, NJ: Institute of Electrical and Electronics Engineers (IEEE), 2020.

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

TY - GEN

T1 - On likelihood functions to minimize KL divergence in binary hypothesis testing

AU - Sun, Linlin

AU - Yan, Shihao

AU - Chen, Riqing

AU - Shu, Feng

PY - 2020

Y1 - 2020

N2 - Kullback-Leibler (KL) divergence is widely used to determine lower bounds on detection error probability for binary hypothesis testing in covert communications and location verification systems. For a Gaussian likelihood function under the null hypothesis H 0 , it has been proved that it is a Gaussian likelihood function under the alternative hypothesis H 1 that minimizes the KL divergence from H 1 to H 0 . Due to the asymmetry of KL divergence, it is still unclear what is the optimal likelihood function under H 1 that minimizes the KL divergence from H 0 to H 1 . Surprisingly, in this work we prove that this optimal likelihood function is unachievable.

AB - Kullback-Leibler (KL) divergence is widely used to determine lower bounds on detection error probability for binary hypothesis testing in covert communications and location verification systems. For a Gaussian likelihood function under the null hypothesis H 0 , it has been proved that it is a Gaussian likelihood function under the alternative hypothesis H 1 that minimizes the KL divergence from H 1 to H 0 . Due to the asymmetry of KL divergence, it is still unclear what is the optimal likelihood function under H 1 that minimizes the KL divergence from H 0 to H 1 . Surprisingly, in this work we prove that this optimal likelihood function is unachievable.

UR - https://www.scopus.com/pages/publications/85100033333

U2 - 10.1109/ICSPCS50536.2020.9310022

DO - 10.1109/ICSPCS50536.2020.9310022

M3 - Conference proceeding contribution

AN - SCOPUS:85100033333

SN - 9781728199719

BT - 2020, 14th International Conference on Signal Processing and Communication Systems, (ICSPCS)

A2 - Wysocki, Tadeusz A.

A2 - Wysocki, Beata J.

PB - Institute of Electrical and Electronics Engineers (IEEE)

CY - Piscataway, NJ

T2 - 14th International Conference on Signal Processing and Communication Systems, ICSPCS 2020

Y2 - 14 December 2020 through 16 December 2020

ER -

On likelihood functions to minimize KL divergence in binary hypothesis testing

Abstract

Conference

Access to Document

Other files and links

Fingerprint

Cite this