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Regularised Least-Squares Regression with Infinite-Dimensional Output Space

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arxiv 2010.10973 v7 pith:5BP23BQH submitted 2020-10-21 stat.ML cs.LG

Junhyunng Park , Krikamol Muandet This is my paper · ORCID
classification stat.MLcs.LG
keywords spacehilbertinfinite-dimensionalnon-compactoutputregressionresultstheory
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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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