Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks

Eric Clarkson

doi:10.1109/IEEECONF51394.2020.9443339

Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks

Eric Clarkson

Medical Imaging

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

Abstract

We have previously shown how the Bayesian Fisher Information (BFI) is related to the average of the Minimum Probability of Error (MPE) for the task of detecting a small change in a parameter. The prior probabilities for the two hypotheses corresponding to two nearby values of the parameter are derived from the prior distribution on the parameter, as they are for the Ziv-Zakai inequality. The average in this result and others to be discussed is performed over the parameter values using the prior. We extend this result to the case where a cost function is assigned to the detection task. In this case we determine the lowest order approximation of the average of the Bayesian Risk for the detection task. We have shown that there is a similar relation between the average Shannon Information (SI) for this detection task and the BFI, and that there is an integral relation between SI for any detection task and the MPE for that task. We will show the Bayesian perspective on this last result, and how these two results about SI are related.

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	1365-1369
Number of pages	5
ISBN (Electronic)	9780738131269
DOIs	https://doi.org/10.1109/IEEECONF51394.2020.9443339
State	Published - Nov 1 2020
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

Keywords

Fisher information
ROC analysis
Shannon information
information theory

ASJC Scopus subject areas

Signal Processing
Computer Networks and Communications

Access to Document

10.1109/IEEECONF51394.2020.9443339

Cite this

Clarkson, E. (2020). Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks. In M. B. Matthews (Ed.), Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020 (pp. 1365-1369). [9443339] (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2020-November). IEEE Computer Society. https://doi.org/10.1109/IEEECONF51394.2020.9443339

Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks. / Clarkson, Eric.
Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020. ed. / Michael B. Matthews. IEEE Computer Society, 2020. p. 1365-1369 9443339 (Conference Record - Asilomar Conference on Signals, Systems and Computers; Vol. 2020-November).

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

Clarkson, E 2020, Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks. in MB Matthews (ed.), Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020., 9443339, Conference Record - Asilomar Conference on Signals, Systems and Computers, vol. 2020-November, IEEE Computer Society, pp. 1365-1369, 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020, Pacific Grove, United States, 11/1/20. https://doi.org/10.1109/IEEECONF51394.2020.9443339

Clarkson E. Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks. In Matthews MB, editor, Conference Record of the 54th Asilomar Conference on Signals, Systems and Computers, ACSSC 2020. IEEE Computer Society. 2020. p. 1365-1369. 9443339. (Conference Record - Asilomar Conference on Signals, Systems and Computers). doi: 10.1109/IEEECONF51394.2020.9443339

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abstract = "We have previously shown how the Bayesian Fisher Information (BFI) is related to the average of the Minimum Probability of Error (MPE) for the task of detecting a small change in a parameter. The prior probabilities for the two hypotheses corresponding to two nearby values of the parameter are derived from the prior distribution on the parameter, as they are for the Ziv-Zakai inequality. The average in this result and others to be discussed is performed over the parameter values using the prior. We extend this result to the case where a cost function is assigned to the detection task. In this case we determine the lowest order approximation of the average of the Bayesian Risk for the detection task. We have shown that there is a similar relation between the average Shannon Information (SI) for this detection task and the BFI, and that there is an integral relation between SI for any detection task and the MPE for that task. We will show the Bayesian perspective on this last result, and how these two results about SI are related.",

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N2 - We have previously shown how the Bayesian Fisher Information (BFI) is related to the average of the Minimum Probability of Error (MPE) for the task of detecting a small change in a parameter. The prior probabilities for the two hypotheses corresponding to two nearby values of the parameter are derived from the prior distribution on the parameter, as they are for the Ziv-Zakai inequality. The average in this result and others to be discussed is performed over the parameter values using the prior. We extend this result to the case where a cost function is assigned to the detection task. In this case we determine the lowest order approximation of the average of the Bayesian Risk for the detection task. We have shown that there is a similar relation between the average Shannon Information (SI) for this detection task and the BFI, and that there is an integral relation between SI for any detection task and the MPE for that task. We will show the Bayesian perspective on this last result, and how these two results about SI are related.

AB - We have previously shown how the Bayesian Fisher Information (BFI) is related to the average of the Minimum Probability of Error (MPE) for the task of detecting a small change in a parameter. The prior probabilities for the two hypotheses corresponding to two nearby values of the parameter are derived from the prior distribution on the parameter, as they are for the Ziv-Zakai inequality. The average in this result and others to be discussed is performed over the parameter values using the prior. We extend this result to the case where a cost function is assigned to the detection task. In this case we determine the lowest order approximation of the average of the Bayesian Risk for the detection task. We have shown that there is a similar relation between the average Shannon Information (SI) for this detection task and the BFI, and that there is an integral relation between SI for any detection task and the MPE for that task. We will show the Bayesian perspective on this last result, and how these two results about SI are related.

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Bayesian Fisher Information, Shannon Information, and ROC Analysis for Classification Tasks

Abstract

Publication series

Conference

Keywords

ASJC Scopus subject areas

Access to Document

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