Geometric Study on Statistical Learning and Computation based on Graphs
| Project/Area Number |
19500249
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Statistical science
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| Research Institution | The Institute of Statistical Mathematics |
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Principal Investigator |
FUKUMIZU Kenji The Institute of Statistical Mathematics, モデリング研究系, 教授 (60311362)
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| Co-Investigator(Kenkyū-buntansha) |
IKEDA Shiro 統計数理研究所, 数理・推論研究系, 准教授 (30336101)
AKAHO Shotaro 産業技術総合研究所, 脳神経情報研究部門, グループ長 (40356340)
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| Project Period (FY) |
2007 – 2009
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| Project Status |
Completed (Fiscal Year 2009)
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| Budget Amount *help |
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2009: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2008: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2007: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Keywords | グラフ / 統計的推論 / 確率伝搬法 / 情報幾何学 / 位相幾何学 / カーネル法 / 再生核ヒルベルト空間 / 機械学習 / ネットワーク学習 / 正定値カーネル / 関数データ / 確率推論 / 情報幾何 |
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| Research Abstract |
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.
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Report
(4 results)
Research Products
(53 results)
