Mathematical Analyses on Sampling Theorems in Reproducing Kernel Hilbert Spaces

2014 Fiscal Year Final Research Report

• Project/Area Number: 24500001
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Fundamental theory of informatics
• Research Institution: Hokkaido University
• Principal Investigator: TANAKA Akira 北海道大学, 情報科学研究科, 准教授 (20332471)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 標本化定理 / 再生核 / 再生核ヒルベルト空間 / 汎化誤差 / アンサンブルカーネル回帰 / マルチカーネル回帰

Outline of Final Research Achievements

It is well known that the sampling theorem plays a crucial role in the field of digital signal processing. In this work, we theoretically analyzed the sampling theory for the reproducing kernel Hilbert spaces. The sampling theorem and the separability of a target function space are two sides of the same coin. We proved that a certain continuity of a reproducing kernel corresponding to the target reproducing kernel Hilbert space guarantees the separability of the reproducing kernel Hilbert space. Recently, function estimation by multiple reproducing kernels attracts much attention in this field. We also analyzed the theoretical properties of such problems and revealed the advantages of the so-called ensemble kernel regression scheme which is a combination of the estimated functions by each reproducing kernel.

Free Research Field

標本化定理