Geometric Study on Statistical Learning and Computation based on Graphs

对图结构描述的数据和概率的推理与计算进行了理论研究，这在复杂结构数据分析中具有重要意义。本文提出了(1)网络结构主动学习方法；(2)引入无限维指数族的柔性推理框架；(3)分析信念传播理论性质的数学方法，即具有图结构的推理算法。这些方法都解决了传统方法难以解决的推理问题和理论性质的阐明。

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.