Structure Learning Theory and Birational Geometry
| Project/Area Number |
23500172
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Intelligent informatics
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
WATANABE SUMIO 東京工業大学, 総合理工学研究科(研究院), 教授 (80273118)
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| Project Period (FY) |
2011-04-28 – 2015-03-31
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| Project Status |
Completed (Fiscal Year 2014)
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| Budget Amount *help |
¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 双有理幾何学 / 構造学習理論 / ベイズ自由エネルギー / WBIC / 双有理不変量 / 代数幾何 / 周辺尤度 / 汎化誤差 / 情報量規準 / 特異揺らぎ / 実対数閾値 / WAIC / 学習理論 / 漸近解析 / 逆温度 |
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| Outline of Final Research Achievements |
In statistical machine learning, it is well known that the appropriate model and prior for a given set of training samples is chosen by minimization of the Bayesian free energy. However, there has been no method to estimate the Bayesian free energy if the posterior distribution can not be approximated by any normal distribution. In this research, we created a new concept, a widely applicable Bayesian information criterion (WBIC), and proved that WBIC has the same asymptotic behavior as the Bayesian free energy, based on the birational geometry. The obtained theorem enables us to choose the optimal model for a given set of training samples, even if the model has hierarchical structures.
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Report
(5 results)
Research Products
(21 results)
