3 papers
math.OC2024
On the Uniqueness of Kantorovich Potentials
Thomas Staudt, Shayan Hundrieser, Axel Munk
Kantorovich potentials denote the dual solutions of the renowned optimal transportation problem. Uniqueness of these solutions is relevant from both a theoretical and an algorithmi…
math.ST2024
Convergence of Empirical Optimal Transport in Unbounded Settings
Thomas Staudt, Shayan Hundrieser
In compact settings, the convergence rate of the empirical optimal transport cost to its population value is well understood for a wide class of spaces and cost functions. In unbou…
stat.ME2024
From Small Scales to Large Scales: Distance-to-Measure Density based Geometric Analysis of Complex Data
Katharina Proksch, Christoph Alexander Weitkamp, Thomas Staudt +2
How can we tell complex point clouds with different small scale characteristics apart, while disregarding global features? Can we find a suitable transformation of such data in a w…