David Krieg, Erich Novak, Mathias Sonnleitner,
"Recovery of Sobolev functions restricted to iid sampling"
, in Math. Comp., Vol. 91, Nummer 338, Seite(n) 2715?2738, 2022
Original Titel:
Recovery of Sobolev functions restricted to iid sampling
Sprache des Titels:
Englisch
Original Kurzfassung:
We study Lq-approximation and integration for functions from
the Sobolev space W^s_p(?) and compare optimal randomized (Monte Carlo) algorithms with algorithms that can only use identically distributed (iid) sample points, uniformly distributed on the domain. The main result is that we obtain the same optimal rate of convergence if we restrict to iid sampling, a common assumption in learning and uncertainty quantification. The only exception is when p=q=?, where a logarithmic loss cannot be avoided.
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