2005 Fiscal Year Final Research Report Summary
Analysis of Belief Propagation algorithms based on Information Geometry
| Project/Area Number |
14084208
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | The National Institute of Advanced Industrial Science and Technology (2003-2005)
Kyushu Institute of Technology (2002) |
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Principal Investigator |
MOTOMURA Yoichi The National Institute of Advanced Industrial Science and Technology Digital Human Research Center, Senior research scientist, デジタルヒューマン研究センター, 主任研究員 (30358171)
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| Co-Investigator(Kenkyū-buntansha) |
IKEDA Shiro Institute of Statistical Mathematics, Department of Mathematical Analysis and Statistical Inference, Associate Professor, 調査解析実験研究系, 助教授 (30336101)
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| Project Period (FY) |
2002 – 2005
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| Keywords | Belief Propagation / Bayesian network / Information geometry / Turbo coding / Low-density parity check code / Probabilistic reasoning / Statistical Learning / EM algorithm |
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| Research Abstract |
In the research of turbo codes, many studies have appeared. Although experimental results strongly support the efficacy of turbo codes, further theoretical analysis is necessary. We extend the geometrical framework initiated by Richardson to the information geometrical framework of dual affine connections, focusing on both of the turbo and LDPC decoding algorithms. The framework helps our intuitive 'understanding of the algorithms and opens a new prospect of further analysis. We reveal some properties of these codes in the proposed framework, including the stability and error analysis. Based on the error analysis, we finally propose a correction term for improving the approximation.
Belief propagation (BP) gives exact inference for stochastic models with tree interactions. Its performance has been analyzed separately in many fields, such as AI, statistical physics, information theory, and information geometry. We give a unified framework for understanding BP and related methods and summ
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arizes the results obtained in many fields. In particular, BP and its variants, including tree reparameterization and concave-convex procedure, are reformulated with information-geometrical terms, and their relations to the free energy function are elucidated from an information-geometrical viewpoint. Then a family of new algorithms are proposed The stabilities of the algorithms are analyzed, and methods to accelerate them are investigated.
Bayesian networks can be utilized for constructing a mathematical model of human cognitive and psychological functions, executable on a computer. We propose probabilistic modeling based on the Personal Construct Theory, a basic theory used in cognitive/evaluative structure models for individuals. After extracting a skeleton structure using the Evaluation Grid, Bayesian network model is constructed though statistical learning. By executing a probabilistic reasoning algorithm using belief propagation on the constructed model, our proposal is applied to user-adaptable information systems, information recommendation, car navigation systems, etc. Less
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Research Products
(11 results)
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[Book] 学習システムの理論と実現2005
Author(s)
渡辺澄夫, 萩原克幸, 赤穂昭太郎, 本村陽一, 福水健次, 岡田真人, 青柳美輝
Total Pages
208
Publisher
森北出版
Description
「研究成果報告書概要(和文)」より
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