A generalized product rule and weak independence based on Bregman divergence

Fujimoto Yu; Murata Noboru

A generalized product rule and weak independence based on Bregman divergence

^*Corresponding author for this work

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

Abstract

To describe the relation between some values, arithmetic operations like multiplication and division are important and conventional tools. These arithmetic operations for probabilities are characterized by the KL divergence, and hence, they can be generalized by using the Bregman divergence instead of the KL divergence. With this idea, independence of random variables is modified by generalized product rule, and a joint probability model is proposed based on this modified weak independence. Effectiveness of weak independent models is shown by numerical experiments on toy examples, and discussed from a geometrical viewpoint.

Original language	English
Title of host publication	WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.
Pages	248-253
Number of pages	6
Publication status	Published - 2008 Dec 1
Event	12th World Multi-Conference on Systemics, Cybernetics and Informatics, WMSCI 2008, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Orlando, FL, United States Duration: 2008 Jun 29 → 2008 Jul 2

Publication series

Name	WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.
Volume	5

Conference

Conference	12th World Multi-Conference on Systemics, Cybernetics and Informatics, WMSCI 2008, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008
Country/Territory	United States
City	Orlando, FL
Period	08/6/29 → 08/7/2

ASJC Scopus subject areas

Artificial Intelligence
Computer Networks and Communications

Cite this

Yu, F., & Noboru, M. (2008). A generalized product rule and weak independence based on Bregman divergence. In WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc. (pp. 248-253). (WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.; Vol. 5).

A generalized product rule and weak independence based on Bregman divergence. / Yu, Fujimoto ; Noboru, Murata.

WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.. 2008. p. 248-253 (WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.; Vol. 5).

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

Yu, F & Noboru, M 2008, A generalized product rule and weak independence based on Bregman divergence. in WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.. WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc., vol. 5, pp. 248-253, 12th World Multi-Conference on Systemics, Cybernetics and Informatics, WMSCI 2008, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008, Orlando, FL, United States, 08/6/29.

Yu F , Noboru M. A generalized product rule and weak independence based on Bregman divergence. In WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.. 2008. p. 248-253. (WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.).

Yu, Fujimoto ; Noboru, Murata. / A generalized product rule and weak independence based on Bregman divergence. WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.. 2008. pp. 248-253 (WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.).

@inproceedings{aeac4c16105543649590326db9f15542,

title = "A generalized product rule and weak independence based on Bregman divergence",

abstract = "To describe the relation between some values, arithmetic operations like multiplication and division are important and conventional tools. These arithmetic operations for probabilities are characterized by the KL divergence, and hence, they can be generalized by using the Bregman divergence instead of the KL divergence. With this idea, independence of random variables is modified by generalized product rule, and a joint probability model is proposed based on this modified weak independence. Effectiveness of weak independent models is shown by numerical experiments on toy examples, and discussed from a geometrical viewpoint.",

author = "Fujimoto Yu and Murata Noboru",

year = "2008",

month = dec,

day = "1",

language = "English",

isbn = "1934272353",

series = "WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.",

pages = "248--253",

booktitle = "WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.",

note = "12th World Multi-Conference on Systemics, Cybernetics and Informatics, WMSCI 2008, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 ; Conference date: 29-06-2008 Through 02-07-2008",

}

TY - GEN

T1 - A generalized product rule and weak independence based on Bregman divergence

AU - Yu, Fujimoto

AU - Noboru, Murata

PY - 2008/12/1

Y1 - 2008/12/1

N2 - To describe the relation between some values, arithmetic operations like multiplication and division are important and conventional tools. These arithmetic operations for probabilities are characterized by the KL divergence, and hence, they can be generalized by using the Bregman divergence instead of the KL divergence. With this idea, independence of random variables is modified by generalized product rule, and a joint probability model is proposed based on this modified weak independence. Effectiveness of weak independent models is shown by numerical experiments on toy examples, and discussed from a geometrical viewpoint.

AB - To describe the relation between some values, arithmetic operations like multiplication and division are important and conventional tools. These arithmetic operations for probabilities are characterized by the KL divergence, and hence, they can be generalized by using the Bregman divergence instead of the KL divergence. With this idea, independence of random variables is modified by generalized product rule, and a joint probability model is proposed based on this modified weak independence. Effectiveness of weak independent models is shown by numerical experiments on toy examples, and discussed from a geometrical viewpoint.

UR - http://www.scopus.com/inward/record.url?scp=84869451599&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84869451599&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:84869451599

SN - 1934272353

SN - 9781934272350

T3 - WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.

SP - 248

EP - 253

BT - WMSCI 2008 - The 12th World Multi-Conference on Systemics, Cybernetics and Informatics, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008 - Proc.

T2 - 12th World Multi-Conference on Systemics, Cybernetics and Informatics, WMSCI 2008, Jointly with the 14th International Conference on Information Systems Analysis and Synthesis, ISAS 2008

Y2 - 29 June 2008 through 2 July 2008

ER -

A generalized product rule and weak independence based on Bregman divergence

Abstract

Publication series

Conference

ASJC Scopus subject areas

Other files and links

Fingerprint

Cite this