2017 Fiscal Year Final Research Report
Statistical mechanics approach to massive sparse modeling
| Project Area | Initiative for High-Dimensional Data-Driven Science through Deepening of Sparse Modeling |
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| Project/Area Number |
25120013
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| Research Category |
Grant-in-Aid for Scientific Research on Innovative Areas (Research in a proposed research area)
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| Allocation Type | Single-year Grants |
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| Review Section |
Complex systems
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
竹田 晃人 茨城大学, 工学部, 准教授 (70397040)
渡邊 澄夫 東京工業大学, 情報理工学院, 教授 (80273118)
坂田 綾香 統計数理研究所, モデリング研究系, 助教 (80733071)
井上 純一 北海道大学, 情報科学研究科, 准教授 (30311658)
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| Co-Investigator(Renkei-kenkyūsha) |
OBUCHI Tomoyuki 東京工業大学, 情報理工学院, 助教 (40588448)
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| Project Period (FY) |
2013-06-28 – 2018-03-31
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| Keywords | 圧縮センシング / 潜在変数モデリング / モデル選択 / レプリカ法 / 平均場近似 / 特異モデル |
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| Outline of Final Research Achievements |
The objective of this project is to develop and systemize methods of multivariate statistics that extract sparse structures lying behind observed data, utilizing the notion of information quantities. In general, one can systematically formulate the statistical-model-based information extraction as optimization problems concerning the information quantities. However, such methods are often computationally difficult to perform in practice. In this project, we intended to practically overcome this difficulty by employing methods and notions of statistical mechanics. By analyzing various concrete models, we aimed to construct a methodology for "systematic" and "practically performable" sparse modeling. Our achievements include performance analysis and algorithm development for various problems that arise in 1) compressive sensing, 2) latent variable models, and 3) issues of model selection.
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| Free Research Field |
統計力学，情報理論，機械学習
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