2009 Fiscal Year Final Research Report
Establishment of Information Physics based on algebraic geometry
| Project/Area Number |
18079007
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| Research Category |
Grant-in-Aid for Scientific Research on Priority Areas
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| Allocation Type | Single-year Grants |
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| Review Section |
Science and Engineering
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
WATANABE Sumio Tokyo Institute of Technology, 精密工学研究所, 教授 (80273118)
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| Co-Investigator(Renkei-kenkyūsha) |
YAMAZAKI Keisuke 東京工業大学, 精密工学研究所, 助教 (60376936)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 代数幾何 / 情報物理学 / 学習理論 / 特異点論 / 超関数論 / 確率過程論 |
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| Research Abstract |
Almost all learning machines used in information science are singular because they have degenerate Fisher Information matrices. Regular statistical theory can not be applied to singular learning machines. In this research, we established new information physics theory for singular learning machines based on higher dimensional algebraic geometry, and clarified that the asymptotic behaviors of generalization and training errors are determined by two birational invariants. Based on new theory, we derived a widely applicable information criterion, by which the generalization error can be estimated from training error in both singular and regular learning machines.
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