Statistical mechanics and sparse modeling approach to large-scale inverse problems
| Project/Area Number |
18K11463
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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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| Review Section |
Basic Section 61040:Soft computing-related
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| Research Institution | Kyoto University (2019-2021)
Tokyo Institute of Technology (2018) |
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Principal Investigator |
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| Project Period (FY) |
2018-04-01 – 2022-03-31
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| Project Status |
Completed (Fiscal Year 2021)
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| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2021: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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)
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| Keywords | 情報統計力学 / スパースモデリング / 統計的逆問題 / 機械学習 / 近似推論 |
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| Outline of Final Research Achievements |
This project has been aimed at obtaining a deeper mathematical understanding and practical numerical solutions to variable selection and parameter estimation problems by extending the techniques of sparse modelling (SpM) and statistical mechanical informatics. As a result, a number of results (16 peer-reviewed papers, including several high impact journals, and three approximation algorithm packages published on Github) have been obtained. In particular, ingenious results include the development and related theoretical analysis of approximation algorithms that perform cross-validation methods with low computational complexity, theoretical analysis of inverse Ising problems related to structural learning, and an approximation algorithm for variable selection using the bootstrap method and its theoretical analysis.
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| Academic Significance and Societal Importance of the Research Achievements |
近年、機械学習や人工知能といったキーワードで、ある種の数学的モデリング方法が注目を集めている。本研究では、そのモデリング方法の中でも、スパースモデリングという、様々な事物(変数)の中から重要なものを半自動的に取りだす技術に着目し、その技術を高めるべく研究を行った。多くの場合、計算量的問題から適切な変数の取り出しが難しくなるのだが、それを情報統計力学という物理分野にある手法で問題を近似することにより、計算量を削減するという方針で研究を行った。その結果、正確性を保ったまま以前よりも速やかに変数選択をすることが可能になった。機械学習を大規模に運用する上で重要な成果と成る。
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Report
(5 results)
Research Products
(39 results)
