Zobrazeno 1 - 10
of 116
pro vyhledávání: '"Gnewuch, Michael"'
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 computationally demanding. Modifying an approach of J. Dick and M. Feischl
Externí odkaz:
http://arxiv.org/abs/2409.13453
We study the integration problem over the $s$-dimensional unit cube on four types of Banach spaces of integrands. First we consider Haar wavelet spaces, consisting of functions whose Haar wavelet coefficients exhibit a certain decay behavior measured
Externí odkaz:
http://arxiv.org/abs/2409.12879
Autor:
Gnewuch, Michael
Publikováno v:
Journal of Complexity, Volume 83, August 2024, 101855
We improve the best known upper bound for the bracketing number of $d$-dimensional axis-parallel boxes anchored in $0$ (or, put differently, of lower left orthants intersected with the $d$-dimensional unit cube $[0,1]^d$). More precisely, we provide
Externí odkaz:
http://arxiv.org/abs/2401.00801
Let $f:[0,1]^d\to\mathbb{R}$ be a completely monotone integrand as defined by Aistleitner and Dick (2015) and let points $\boldsymbol{x}_0,\dots,\boldsymbol{x}_{n-1}\in[0,1]^d$ have a non-negative local discrepancy (NNLD) everywhere in $[0,1]^d$. We
Externí odkaz:
http://arxiv.org/abs/2309.04209
According to Aistleitner and Weimar, there exist two-dimensional (double) infinite matrices whose star-discrepancy $D_N^{*s}$ of the first $N$ rows and $s$ columns, interpreted as $N$ points in $[0,1]^s$, satisfies an inequality of the form $$D_N^{*s
Externí odkaz:
http://arxiv.org/abs/2305.04686
We study integration and $L^2$-approximation of functions of infinitely many variables in the following setting: The underlying function space is the countably infinite tensor product of univariate Hermite spaces and the probability measure is the co
Externí odkaz:
http://arxiv.org/abs/2304.01754
We consider $L^2$-approximation on weighted reproducing kernel Hilbert spaces of functions depending on infinitely many variables. We focus on unrestricted linear information, admitting evaluations of arbitrary continuous linear functionals. We disti
Externí odkaz:
http://arxiv.org/abs/2301.13177
Autor:
Doerr, Benjamin, Gnewuch, Michael
Publikováno v:
Journal of Complexity, Vol. 67 (2021), 101589
We study the notion of $\gamma$-negative dependence of random variables. This notion is a relaxation of the notion of negative orthant dependence (which corresponds to $1$-negative dependence), but nevertheless it still ensures concentration of measu
Externí odkaz:
http://arxiv.org/abs/2104.10799
Autor:
Gnewuch, Michael, Hebbinghaus, Nils
Publikováno v:
The Annals of Applied Probability, vol. 31, no. 4 (2021), 1944-1965
We introduce a class of $\gamma$-negatively dependent random samples. We prove that this class includes, apart from Monte Carlo samples, in particular Latin hypercube samples and Latin hypercube samples padded by Monte Carlo. For a $\gamma$-negativel
Externí odkaz:
http://arxiv.org/abs/2102.04451
Publikováno v:
Mathematics of Computation 90 (2021), 2873-2898
We prove a generalized Faulhaber inequality to bound the sums of the $j$-th powers of the first $n$ (possibly shifted) natural numbers. With the help of this inequality we are able to improve the known bounds for bracketing numbers of $d$-dimensional
Externí odkaz:
http://arxiv.org/abs/2010.11479