2013 Fiscal Year Final Research Report
Mathematical foundation of efficient algorithms for statistical inference
| Project/Area Number |
22300098
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 統計数理研究所, 大学共同利用機関等の部局等, 教授 (60311362)
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| Co-Investigator(Kenkyū-buntansha) |
TANAKA Toshiyuki 京都大学, 情報学研究科, 教授 (10254153)
IKEDA Shiro 統計数理研究所, 数理・推論研究系, 准教授 (30336101)
KABASHIMA Yoshiyuki 東京工業大学, 総合理工学研究科, 教授 (80260652)
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| Project Period (FY) |
2010-04-01 – 2014-03-31
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| Keywords | グラフ / アルゴリズム / 確率計算 / 情報幾何 / 位相幾何 |
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| Research Abstract |
As a new mathematical method for analyzing propagation algorithms on graphs, a novel Graph zeta function has been proposed for the analysis of the loopy belief propagation algorithm, and used for revealing stronger theoretical results than the known ones. Also, a method of loop expansion has been proposed for analyzing the approximation error of the loopy belief propagation.
As a mathematical foundation of the expectation propagation, an infinite dimensional exponential family has been proposed based on positive definite kernels, and its estimation methods and theoretical properties have been studied.
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