Application of Kähler manifold to signal processing and Bayesian inference

Jaehyung Choi; Andrew P. Mullhaupt

doi:10.1063/1.4905970

Application of Kähler manifold to signal processing and Bayesian inference

Jaehyung Choi
, Andrew P. Mullhaupt

Applied Mathematics and Statistics

Stony Brook University

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

2 Scopus citations

Abstract

We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such as α-divergence, information distance and the dual α-connection structure. The Kähler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the α-generalization of the geometric objects. The Laplace-Beltrami operator is also simplified in the Kähler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the Kähler structure.

Original language	English
Title of host publication	Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014
Editors	Ali Mohammad-Djafari, Frederic Barbaresco, Frederic Barbaresco
Publisher	American Institute of Physics Inc.
Pages	113-120
Number of pages	8
ISBN (Electronic)	9780735412804
DOIs	https://doi.org/10.1063/1.4905970
State	Published - 2015
Event	34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014 - Amboise, France Duration: Sep 21 2014 → Sep 26 2014

Publication series

Name	AIP Conference Proceedings
Volume	1641
ISSN (Print)	0094-243X
ISSN (Electronic)	1551-7616

Conference

Conference	34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014
Country/Territory	France
City	Amboise
Period	09/21/14 → 09/26/14

Keywords

ARFIMA model
Bayesian inference
information geometry
Komaki prior
Kähler manifold
signal processing

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10.1063/1.4905970

Cite this

Choi, J., & Mullhaupt, A. P. (2015). Application of Kähler manifold to signal processing and Bayesian inference. In A. Mohammad-Djafari, F. Barbaresco, & F. Barbaresco (Eds.), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014 (pp. 113-120). (AIP Conference Proceedings; Vol. 1641). American Institute of Physics Inc.. https://doi.org/10.1063/1.4905970

@inproceedings{7266d10ed1654ceeb3c82aaa511483e9,

title = "Application of K{\"a}hler manifold to signal processing and Bayesian inference",

abstract = "We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the K{\"a}hler manifold case. We find conditions for the information geometry of linear systems to be K{\"a}hler, and the relation of the K{\"a}hler potential to information geometric quantities such as α-divergence, information distance and the dual α-connection structure. The K{\"a}hler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the α-generalization of the geometric objects. The Laplace-Beltrami operator is also simplified in the K{\"a}hler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the K{\"a}hler structure.",

keywords = "ARFIMA model, Bayesian inference, information geometry, Komaki prior, K{\"a}hler manifold, signal processing",

author = "Jaehyung Choi and Mullhaupt, \{Andrew P.\}",

note = "Publisher Copyright: {\textcopyright} 2015 AIP Publishing LLC.; 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014 ; Conference date: 21-09-2014 Through 26-09-2014",

year = "2015",

doi = "10.1063/1.4905970",

language = "English",

series = "AIP Conference Proceedings",

publisher = "American Institute of Physics Inc.",

pages = "113--120",

editor = "Ali Mohammad-Djafari and Frederic Barbaresco and Frederic Barbaresco",

booktitle = "Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014",

}

Choi, J & Mullhaupt, AP 2015, Application of Kähler manifold to signal processing and Bayesian inference. in A Mohammad-Djafari, F Barbaresco & F Barbaresco (eds), Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014. AIP Conference Proceedings, vol. 1641, American Institute of Physics Inc., pp. 113-120, 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014, Amboise, France, 09/21/14. https://doi.org/10.1063/1.4905970

Application of Kähler manifold to signal processing and Bayesian inference. / Choi, Jaehyung; Mullhaupt, Andrew P.
Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014. ed. / Ali Mohammad-Djafari; Frederic Barbaresco; Frederic Barbaresco. American Institute of Physics Inc., 2015. p. 113-120 (AIP Conference Proceedings; Vol. 1641).

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

TY - GEN

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AU - Choi, Jaehyung

AU - Mullhaupt, Andrew P.

PY - 2015

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N2 - We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such as α-divergence, information distance and the dual α-connection structure. The Kähler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the α-generalization of the geometric objects. The Laplace-Beltrami operator is also simplified in the Kähler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the Kähler structure.

AB - We review the information geometry of linear systems and its application to Bayesian inference, and the simplification available in the Kähler manifold case. We find conditions for the information geometry of linear systems to be Kähler, and the relation of the Kähler potential to information geometric quantities such as α-divergence, information distance and the dual α-connection structure. The Kähler structure simplifies the calculation of the metric tensor, connection, Ricci tensor and scalar curvature, and the α-generalization of the geometric objects. The Laplace-Beltrami operator is also simplified in the Kähler geometry. One of the goals in information geometry is the construction of Bayesian priors outperforming the Jeffreys prior, which we use to demonstrate the utility of the Kähler structure.

KW - ARFIMA model

KW - Bayesian inference

KW - information geometry

KW - Komaki prior

KW - Kähler manifold

KW - signal processing

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DO - 10.1063/1.4905970

M3 - Conference contribution

AN - SCOPUS:85063816355

T3 - AIP Conference Proceedings

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EP - 120

BT - Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014

A2 - Mohammad-Djafari, Ali

A2 - Barbaresco, Frederic

PB - American Institute of Physics Inc.

T2 - 34th International Workshop on Bayesian Inference and Maximum Entropy Methods in Science and Engineering, MaxEnt 2014

Y2 - 21 September 2014 through 26 September 2014

ER -

Application of Kähler manifold to signal processing and Bayesian inference

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Keywords

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