Geometric Study on Statistical Learning and Computation based on Graphs

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Theoretical study was carried out on the inference and computation of data and probabilities described by graph structures, which is of importance in analyzing data of complex structure. This study proposed (1)a method of active learning of network structure, (2)a framework of flexible inference by introducing infinite dimensional exponential families, and (3)a mathematical method for analyzing theoretical properties of the belief propagation, which is an inference algorithm with graph structure. Each of these methods provided solutions to inference problems and elucidation of theoretical properties, which had been difficult by conventional methods.