15 citations · 53 across the 11 of their papers we have counts for
13 papers
Wasserstein Gradient Flows of the Discrepancy with Distance Kernel on the Line
Johannes Hertrich, Robert Beinert, Manuel Gräf +1
This paper provides results on Wasserstein gradient flows between measures on the real line. Utilizing the isometric embedding of the Wasserstein space in…
Wasserstein Steepest Descent Flows of Discrepancies with Riesz Kernels
Johannes Hertrich, Manuel Gräf, Robert Beinert +1
The aim of this paper is twofold. Based on the geometric Wasserstein tangent space, we first introduce Wasserstein steepest descent flows. These are locally absolutely continuous c…
On the Dynamical System of Principal Curves in
Robert Beinert, Arian Bërdëllima, Manuel Gräf +1
Principal curves are natural generalizations of principal lines arising as first principal components in the Principal Component Analysis. They can be characterized from a stochast…
Curve Based Approximation of Measures on Manifolds by Discrepancy Minimization
Martin Ehler, Manuel Gräf, Sebastian Neumayer +1
The approximation of probability measures on compact metric spaces and in particular on Riemannian manifoldsby atomic or empirical ones is a classical task in approximation and com…
Spectral decomposition of discrepancy kernels on the Euclidean ball, the special orthogonal group, and the Grassmannian manifold
Josef Dick, Martin Ehler, Manuel Gräf +1
To numerically approximate Borel probability measures by finite atomic measures, we study the spectral decomposition of discrepancy kernels when restricted to compact subsets of $\…
Optimal Monte Carlo integration on closed manifolds
Martin Ehler, Manuel Graef, Chris. J. Oates
The worst case integration error in reproducing kernel Hilbert spaces of standard Monte Carlo methods with n random points decays as . However, re-weighting of random poi…
Cubatures on Grassmannians: moments, dimension reduction, and related topics
Anna Breger, Martin Ehler, Manuel Graef +1
We briefly explain the use of cubature points on Grassmannians in numerical analysis.
Points on manifolds with asymptotically optimal covering radius
Anna Breger, Martin Ehler, Manuel Graef
Given a finite set of points on the Euclidean sphere, the worst case quadrature error in Sobolev spaces has recently been shown to provide upper bounds on the covering radius of th…
Quasi Monte Carlo integration and kernel-based function approximation on Grassmannians
Anna Breger, Martin Ehler, Manuel Graef
Numerical integration and function approximation on compact Riemannian manifolds based on eigenfunctions of the Laplace-Beltrami operator have been widely studied in the recent lit…
From low to high-dimensional moments without magic
Bernhard G. Bodmann, Martin Ehler, Manuel Graef
We aim to compute the first few moments of a high-dimensional random vector from the first few moments of a number of its low-dimensional projections. To this end, we identify alge…
Phase retrieval using random cubatures and fusion frames of positive semidefinite matrices
Martin Ehler, Manuel Graef, Franz J. Kiraly
As a generalization of the standard phase retrieval problem, we seek to reconstruct symmetric rank-1 matrices from inner products with subclasses of positive semidefinite matrices.…
Optimal configurations of lines and a statistical application
François Bachoc, Martin Ehler, Manuel Gräf
Motivated by the construction of confidence intervals in statistics, we study optimal configurations of lines in real projective space . For small , we determi…
Reproducing kernels for the irreducible components of polynomial spaces on unions of Grassmannians
Martin Ehler, Manuel Gräf
The decomposition of polynomial spaces on unions of Grassmannians into irreducible orthogonally invariant subspaces and th…