Mathematical Properties of Sampling and Optimal Reproducing Kernels
Project/Area Number |
21700001
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Research Category |
Grant-in-Aid for Young Scientists (B)
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Allocation Type | Single-year Grants |
Research Field |
Fundamental theory of informatics
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Research Institution | Hokkaido University |
Principal Investigator |
TANAKA Akira 北海道大学, 大学院・情報科学研究科, 准教授 (20332471)
|
Project Period (FY) |
2009 – 2011
|
Project Status |
Completed (Fiscal Year 2011)
|
Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2011: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2010: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2009: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
|
Keywords | 情報数理 / 標本化定理 / 再生核ヒルベルト空間 / 機械学習 / 標本化 / 再生核 / ヒルベルト空間 / モデル選択 / 計量 / 直交射影 / 汎化誤差 / 関数推定 / グラム行列 |
Research Abstract |
In this work, we theoretically analyzed properties of sampling theories for reproducing kernel Hilbert spaces(RKHS's). Our main contributions are1) we gave a necessary and sufficient condition for a given RKHS and a given set of sampling points to satisfy the sampling theorem, 2) we gave an upper bound of errors in case that the sampling theorem does not hold, and3) we clarified the behavior of the solution in various machine learning problems with respect to sampling points and an adopted RKHS.
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Report
(4 results)
Research Products
(39 results)