2016 Fiscal Year Final Research Report
A comprehensive study of learning, inference, and inverse problems based on the spin-glass theory
| Project/Area Number |
26870185
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Multi-year Fund |
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| Research Field |
Theory of informatics
Mathematical physics/Fundamental condensed matter physics
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Project Period (FY) |
2014-04-01 – 2017-03-31
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| Keywords | 逆問題・多自由度推定 / 統計的学習理論・機械学習 / 統計物理学 / 最大エントロピー法 / スパースモデリング |
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| Outline of Final Research Achievements |
The purpose of this study is to clarify general and theoretical aspects of statistical learning theory and inverse problems by using the spin-glass theory from statistical physics. The objective of the discipline is to infer a correct probability distribution from a limited number of observations. Hence common important theoretical questions are as follows: Clarifying the achievable theoretic limit given the limited observations; designing algorithms to achieve the limit; applying the algorithms to real-world dataset.
Our actual research processes were roughly categorized into two processes: One is to clarify the theoretical limit by utilizing the spin-glass theory; the other is to invent algorithms and apply them to neurons' firing data and natural image processing.
Our study has clarified that two commonly used frameworks, the maximum entropy principle and sparse modelling, have their own theoretical limits and have contrasting pros and cons.
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| Free Research Field |
統計物理学
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