2023 Fiscal Year Final Research Report
New estimation of hyperparameters for support vector regression
| Project/Area Number |
22K17860
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| Research Category |
Grant-in-Aid for Early-Career Scientists
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| Allocation Type | Multi-year Fund |
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| Review Section |
Basic Section 60030:Statistical science-related
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| Research Institution | Chuo University (2023)
Yokohama City University (2022) |
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Principal Investigator |
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| Project Period (FY) |
2022-04-01 – 2024-03-31
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| Keywords | カーネル法 / サポートベクター回帰 / 漸近理論 / 再生核ヒルベルト空間 / 機械学習 |
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| Outline of Final Research Achievements |
In this study, we focused on the problem of parameter estimation in one of the kernel methods, specifically Support Vector Regression (SVR). We developed a method to estimate the parameters of nonlinear Support Vector Regression using penalized likelihood and derived several lemmas to establish the theoretical foundation. Additionally, through the application to real datasets, we confirmed that the method is sufficiently practical for actual data applications. For the sake of theoretical research, we also conducted studies related to Reproducing Kernel Hilbert Spaces (RKHS) beyond just Support Vector Regression.
During the research period, we made seven conference presentations and had one paper accepted and published. With the support of the Grants-in-Aid for Scientific Research (KAKENHI), we were able to achieve these results.
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| Free Research Field |
数理統計学
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| Academic Significance and Societal Importance of the Research Achievements |
非線形サポートベクター回帰のパラメータを決定するにあたってよく知られている方法としては，クロスバリデーション法と呼ばれる方法である．この方法では，候補となるあらゆるパラメータでの回帰を行い，その回帰についての評価を行う．あらゆる組み合わせにおける回帰を計算する必要があるため，非線形サポートベクター回帰のような選択すべきパラメータが多い手法において計算量が非常に多くなるという問題点が挙げられていた．このため，本研究の成果はこの問題点を解決する手法の一つとなっている．さらに，サポートベクター回帰のような機械学習手法はAI技術としても用いられており，昨今の科学技術発展につながる．
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