Analysis of Belief Propagation algorithms based on Information Geometry

在Turbo码的研究中，出现了许多研究成果。虽然实验结果强烈支持Turbo码的有效性，但还需要进一步的理论分析。本文将Richardson提出的几何框架推广到对偶仿射连接的信息几何框架，重点研究了Turbo码和LDPC码的译码算法。该框架有助于我们对算法的直观理解，并为进一步的分析开辟了新的前景。我们揭示了这些代码在建议的框架，包括稳定性和错误分析的一些性质。在误差分析的基础上，我们提出了一个修正项来改进近似。它的性能已经在许多领域分别进行了分析，如人工智能，统计物理，信息论和信息几何。我们给出了一个统一的框架来理解BP和相关的方法，并总结了 ...更多信息 总结了在许多领域取得的成果。特别是，BP及其变种，包括树重新参数化和凹凸过程，重新制定与信息几何条款，并阐明它们的自由能函数的关系，从信息几何的观点。然后提出了一系列新的算法，分析了算法的稳定性，研究了加速算法的方法.贝叶斯网络可用于构造人类认知和心理功能的数学模型，可在计算机上执行.我们提出了基于个人建构理论，用于个人的认知/评价结构模型的基本理论的概率建模。在利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。通过执行一个概率推理算法，使用信念传播的构造模型，我们的建议是适用于用户自适应信息系统，信息推荐，汽车导航系统等。

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