12 citations · 26 across the 10 of their papers we have counts for
11 papers
Sharp bounds for non-adaptive randomized approximation of high-dimensional vectors
Robert J. Kunsch, Marcin Wnuk
We study the complexity of approximating the finite-dimensional vector space embedding for based on non-adaptive rand…
Adaptive and non-adaptive randomized approximation of high-dimensional vectors
Robert J. Kunsch, Marcin Wnuk
We study approximation of the embedding , , based on randomized algorithms that use up to arbitrary linear function…
Data Compression using Rank-1 Lattices for Parameter Estimation in Machine Learning
Michael Gnewuch, Kumar Harsha, Marcin Wnuk
The mean squared error and regularized versions of it are standard loss functions in supervised machine learning. However, calculating these losses for large data sets can be compu…
Uniform approximation of vectors using adaptive randomized information
Robert J. Kunsch, Marcin Wnuk
We study approximation of the embedding , , based on randomized adaptive algorithms that use arbitrary linear functionals as…
Randomized approximation of summable sequences -- adaptive and non-adaptive
Robert Kunsch, Erich Novak, Marcin Wnuk
We prove lower bounds for the randomized approximation of the embedding based on algorithms that use arbitrary linear (hence non-adaptive) info…
Infinite-Variate -Approximation with Nested Subspace Sampling
Kumar Harsha, Michael Gnewuch, Marcin Wnuk
We consider -approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admi…
A short note on compact embeddings of reproducing kernel Hilbert spaces in for infinite-variate function approximation
Marcin Wnuk
This note consists of two largely independent parts. In the first part we give conditions on the kernel of a reproducing kernel Hilbert space $…
Randomized sparse grid algorithms for multivariate integration on Haar-Wavelet spaces
Marcin Wnuk, Michael Gnewuch
The \emph{deterministic} sparse grid method, also known as Smolyak's method, is a well-established and widely used tool to tackle multivariate approximation problems, and there is…
On Negatively Dependent Sampling Schemes, Variance Reduction, and Probabilistic Upper Discrepancy Bounds
Michael Gnewuch, Marcin Wnuk, Nils Hebbinghaus
We study some notions of negative dependence of a sampling scheme that can be used to derive variance bounds for the corresponding estimator or discrepancy bounds for the underlyin…
Note on Pairwise Negative Dependence of Randomized Rank-1 Lattices
Marcin Wnuk, Michael Gnewuch
In her recent paper [Negative dependence, scrambled nets, and variance bounds. Math. Oper. Res. 43 (2018), 228-251] Christiane Lemieux studied a framework to analyze the dependence…
Explicit error bounds for randomized Smolyak algorithms and an application to infinite-dimensional integration
Michael Gnewuch, Marcin Wnuk
Smolyak's method, also known as hyperbolic cross approximation or sparse grid method, is a powerful tool to tackle multivariate tensor product problems solely with the help of effi…