938 citations · 1.2k across the 21 of their papers we have counts for
26 papers
New lower bounds for the integration of periodic functions
David Krieg, Jan Vybiral
We study the integration problem on Hilbert spaces of (multivariate) periodic functions. The standard technique to prove lower bounds for the error of quadrature rules uses bump fu…
Lower bounds for integration and recovery in
Aicke Hinrichs, David Krieg, Erich Novak +1
Function values are, in some sense, "almost as good" as general linear information for -approximation (optimal recovery, data assimilation) of functions from a reproducing ker…
A variant of Schur's product theorem and its applications
Jan Vybíral
We show the following version of the Schur's product theorem. If is a positive semidefinite matrix with all entries on the diagona…
On the volume of unit balls of finite-dimensional Lorentz spaces
Anna Doležalová, Jan Vybíral
We study the volume of unit balls of finite-dimensional Lorentz sequence spaces We give an iterative formula for for the weak Leb…
Deterministic constructions of high-dimensional sets with small dispersion
Mario Ullrich, Jan Vybíral
The dispersion of a point set is the volume of the largest box with sides parallel to the coordinate axes, which does not intersect . Here, we show a construct…
The minimal -dispersion of point sets in high-dimensions
Aicke Hinrichs, Joscha Prochno, Mario Ullrich +1
In this manuscript we introduce and study an extended version of the minimal dispersion of point sets, which has recently attracted considerable attention. Given a set $\mathscr P_…
Learning general sparse additive models from point queries in high dimensions
Hemant Tyagi, Jan Vybiral
We consider the problem of learning a -variate function defined on the cube , where the algorithm is assumed to have black box access to sampl…
An upper bound on the minimal dispersion
Mario Ullrich, Jan Vybíral
For and a natural number , let be a natural number with \[ N \,\ge\, 2^9\,\log_2(d)\, \left(\frac{\log_2(1/\varepsilon)}{\varepsilon}\right)^2.…
Entropy numbers of embeddings of Schatten classes
Aicke Hinrichs, Joscha Prochno, Jan Vybiral
Let and denote by and the corresponding finite-dimensional Schatten classes. We prove optimal bounds, up to constants only dep…
Learning physical descriptors for materials science by compressed sensing
Luca M. Ghiringhelli, Jan Vybiral, Emre Ahmetcik +4
The availability of big data in materials science offers new routes for analyzing materials properties and functions and achieving scientific understanding. Finding structure in th…
Random Matrices and Matrix Completion
Jan Vybiral
The aim of this note (as well as of the course itself) is to give a largely self-contained proof of two of the main results in the field of low-rank matrix recovery. This field aim…
Carl's inequality for quasi-Banach spaces
Aicke Hinrichs, Anton Kolleck, Jan Vybiral
We prove that for any two quasi-Banach spaces and and any there exists a constant such that $$ \sup_{1\le k\le n}k^αe_k(T)\le γ_α\sup_{1\le k\le n} k^αc_k(T)…
Non-asymptotic Analysis of -norm Support Vector Machines
Anton Kolleck, Jan Vybíral
Support Vector Machines (SVM) with penalty became a standard tool in analysis of highdimensional classification problems with sparsity constraints in many applications inc…
Sparse Proteomics Analysis - A compressed sensing-based approach for feature selection and classification of high-dimensional proteomics mass spectrometry data
Tim Conrad, Martin Genzel, Nada Cvetkovic +5
Background: High-throughput proteomics techniques, such as mass spectrometry (MS)-based approaches, produce very high-dimensional data-sets. In a clinical setting one is often inte…
Big Data of Materials Science - Critical Role of the Descriptor
Luca M. Ghiringhelli, Jan Vybiral, Sergey V. Levchenko +2
Statistical learning of materials properties or functions so far starts with a largely silent, non-challenged step: the choice of the set of descriptive parameters (termed descript…
On some aspects of approximation of ridge functions
Anton Kolleck, Jan Vybiral
We present effective algorithms for uniform approximation of multivariate functions satisfying some prescribed inner structure. We extend in several directions the analysis of reco…
Entropy and sampling numbers of classes of ridge functions
Sebastian Mayer, Tino Ullrich, Jan Vybiral
We study properties of ridge functions in high dimensions from the viewpoint of approximation theory. The considered function classes consist of ridge functi…
Weak and quasi-polynomial tractability of approximation of infinitely differentiable functions
Jan Vybiral
We comment on recent results in the field of information based complexity, which state (in a number of different settings), that approximation of infinitely differentiable function…
The Characterization of Radial Subspaces of Besov- and Lizorkin-Triebel Spaces by Differences
Winfried Sickel, Leszek Skrzypczak, Jan Vybiral
We continue our earlier investigations of radial subspaces of Besov and Lizorkin-Triebel spaces on . This time we study characterizations of these subspaces by differences.
Complex Interpolation of Weighted Besov- and Lizorkin-Triebel Spaces (long version)
Winfried Sickel, Leszek Skrzypczak, Jan Vybiral
We study complex interpolation of weighted Besov and Lizorkin-Triebel spaces. The used weights are local Muckenhoupt weights in the sense of Rychkov. As a first step we c…
Particle systems and kinetic equations modeling interacting agents in high dimension
Massimo Fornasier, Jan Haskovec, Jan Vybiral
In this paper we explore how concepts of high-dimensional data compression via random projections onto lower-dimensional spaces can be applied for tractable simulation of certain d…
Spaces of variable smoothness and integrability: Characterizations by local means and ball means of differences
Henning Kempka, Jan Vybiral
We study the spaces of Besov and Triebel-Lizorkin type with variable smoothness and integrability as introduced recently by Almeida & Hästö and Diening, Hästö & Roudenko. Both scal…
A note on the spaces of variable integrability and summability of Almeida and Hästö
Henning Kempka, Jan Vybiral
We address an open problem posed recently by Almeida and Hästö in \cite{AlHa10}. They defined the spaces $\ellqp$ of variable integrability and summability and showed that $\|\cdot…
Average best -term approximation
Jan Vybíral
We introduce the concept of average best -term approximation widths with respect to a probability measure on the unit ball of . We estimate these quantities for the em…