Analysis of Belief Propagation algorithms based on Information Geometry

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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