Regularised Least-Squares Regression with Infinite-Dimensional Output Space

• URL: http://arxiv.org/abs/2010.10973v7
• Date: Wed, 16 Feb 2022 06:11:15 GMT
• Title: Regularised Least-Squares Regression with Infinite-Dimensional Output Space
• Authors: Junhyunng Park and Krikamol Muandet
• Abstract summary: This report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression. Our approach is based on the integral operator technique using spectral theory for non-compact operators.
• Score: 8.556182714884567
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This short technical report presents some learning theory results on vector-valued reproducing kernel Hilbert space (RKHS) regression, where the input space is allowed to be non-compact and the output space is a (possibly infinite-dimensional) Hilbert space. Our approach is based on the integral operator technique using spectral theory for non-compact operators. We place a particular emphasis on obtaining results with as few assumptions as possible; as such we only use Chebyshev's inequality, and no effort is made to obtain the best rates or constants.

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