Breakthrough of limits in compressed sensing by the picture of phase transition
| Project/Area Number |
17K12749
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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 |
Soft computing
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| Research Institution | Doshisha University (2021)
The University of Tokyo (2017-2020) |
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Principal Investigator |
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| Project Period (FY) |
2017-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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| Keywords | 圧縮センシング / スパースモデリング / 交差検証 / ハイパーパラメータ / LASSO / 統計力学 / 状態方程式 / 相転移 / ベイズ推論 |
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| Outline of Final Research Achievements |
This research developed a cross-validation based method for judging the success or failure of compressed sensing, considering practical situations where compressed sensing with sparse modeling is applied to unknown objects. Analysis with the replica method from statistical mechanics revealed a power-law behavior of cross-validation error at the transition point in the amount of available data from the failure to the success of compressed sensing. This research proposed judging the success or failure in compressed sensing based on the dependence of cross-validation error on the amount ratio between training and validation datasets in cross validation and evaluated the performance of the proposed method by numerical experiments.
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| Academic Significance and Societal Importance of the Research Achievements |
本研究の成果として、圧縮センシングの限界が明らかになったことにより、不十分なデータによる誤った解析結果を鵜呑みにすることなく、またデータが十分であることを認識できずに過剰なデータ取得に陥るようなこともなくなると考えられる。本研究で開発した手法は交差検証に基づいており、スパースモデリングに限らずあらゆる情報学的手法と組み合わせて用いることができる。圧縮センシングの他にも情報学的手法を用いた実験・計測の効率化は試みられており、そのような場合にも発展する可能性がある。
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Report
(6 results)
Research Products
(40 results)
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[Journal Article] ES-DoS: Exhaustive search and density-of-states estimation as a general framework for sparse variable selection.2018
Author(s)
Igarashi, Y., Ichikawa, H., Nakanishi-Ohno, Y., Takenaka, H., Kawabata, D., Eifuku, S., Tamura, R., Nagata, K., & Okada, M.
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Journal Title
Journal of Physics: Conference Series.
Volume: 1036
Pages: 1-13
DOI
Related Report
Peer Reviewed / Open Access
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