2021
DOI: 10.1007/s10208-021-09529-5
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Distributed Learning via Filtered Hyperinterpolation on Manifolds

Abstract: Learning mappings of data on manifolds is an important topic in contemporary machine learning, with applications in astrophysics, geophysics, statistical physics, medical diagnosis, biochemistry, and 3D object analysis. This paper studies the problem of learning real-valued functions on manifolds through filtered hyperinterpolation of input–output data pairs where the inputs may be sampled deterministically or at random and the outputs may be clean or noisy. Motivated by the problem of handling large data sets… Show more

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Cited by 4 publications
(2 citation statements)
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“…We refer the reader to [17,19,21,29,32,36,37,42] for some follow-up works on the general analysis of hyperinterpolation and [2,22,28,38] for some variants of classical hyperinterpolation.…”
Section: The Approximation Basicsmentioning
confidence: 99%
See 1 more Smart Citation
“…We refer the reader to [17,19,21,29,32,36,37,42] for some follow-up works on the general analysis of hyperinterpolation and [2,22,28,38] for some variants of classical hyperinterpolation.…”
Section: The Approximation Basicsmentioning
confidence: 99%
“…The fact that L n ∞ is not uniformly bounded has spurred the development of filtered hyperinterpolation on the sphere and then on general regions [22,28,38]. The filtered hyperinterpolation operator, as an operator from C(Ω) → C(Ω), has a uniformly bounded norm.…”
Section: Remark 52mentioning
confidence: 99%