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Analysis of Belief Propagation algorithms based on Information Geometry

基于信息几何的置信传播算法分析

基本信息

批准号：
14084208
负责人：
MOTOMURA Yoichi
金额：
$ 4.22万
依托单位：
The National Institute of Advanced Industrial Science and Technology (2003-2005)Kyushu Institute of Technology (2002)
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research on Priority Areas
财政年份：
2002
资助国家：
日本
起止时间：
2002 至 2005
项目状态：
已结题

项目摘要

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 … More 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

在Turbo码的研究中，出现了许多研究成果。虽然实验结果有力地支持了Turbo码的有效性，但还需要进一步的理论分析。我们将Richardson提出的几何框架扩展到双仿射连接的信息几何框架，重点研究了Turbo和LDPC译码算法。该框架有助于我们对算法的直观理解，并为进一步分析开辟了新的前景。在所提出的框架下，我们揭示了这些码的一些性质，包括稳定性和误差分析。在误差分析的基础上，提出了一种改进近似的修正项.对于具有树相互作用的随机模型，信念传播(BP)给出了精确的推断.在人工智能、统计物理、信息论、信息几何等多个领域分别对其性能进行了分析。给出了一个理解BP及其相关方法的统一框架，并概述了…进一步推广了在许多领域所取得的结果。特别地，BP及其变体，包括树的重新参数化和凹凸过程，被重新表述为信息几何项，并从信息几何的角度阐明了它们与自由能函数的关系。然后提出了一系列新的算法，分析了算法的稳定性，并研究了加速算法的方法。贝叶斯网络可用于构建可在计算机上执行的人类认知和心理功能的数学模型。我们提出了基于个人建构理论的概率建模，该理论是用于个体认知/评价结构模型的基本理论。在使用评估网格提取骨架结构后，通过统计学习构建贝叶斯网络模型。通过在构建的模型上执行基于信任传播的概率推理算法，我们的建议被应用于用户自适应的信息系统、信息推荐、汽车导航系统等