13 citations · 42 across the 9 of their papers we have counts for
9 papers
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…
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…
A Unifying Approach to Distributional Limits for Empirical Optimal Transport
Shayan Hundrieser, Marcel Klatt, Thomas Staudt +1
We provide a unifying approach to central limit type theorems for empirical optimal transport (OT). In general, the limit distributions are characterized as suprema of Gaussian pro…
Empirical Optimal Transport between Different Measures Adapts to Lower Complexity
Shayan Hundrieser, Thomas Staudt, Axel Munk
The empirical optimal transport (OT) cost between two probability measures from random data is a fundamental quantity in transport based data analysis. In this work, we derive nove…
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…
Transport Dependency: Optimal Transport Based Dependency Measures
Thomas Giacomo Nies, Thomas Staudt, Axel Munk
Finding meaningful ways to measure the statistical dependency between random variables and is a timeless statistical endeavor. In recent years, several novel concepts, like…
Statistical Molecule Counting in Super-Resolution Fluorescence Microscopy: Towards Quantitative Nanoscopy
Thomas Staudt, Timo Aspelmeier, Oskar Laitenberger +3
Super-resolution microscopy is rapidly gaining importance as an analytical tool in the life sciences. A compelling feature is the ability to label biological units of interest with…
Posterior Consistency in the Binomial Model with Unknown and : A Numerical Study
Laura Fee Schneider, Thomas Staudt, Axel Munk
Estimating the parameters from independent Bin random variables, when both parameters and are unknown, is relevant to a variety of applications. It is particular…
Posterior analysis of in the binomial problem with both parameters unknown -- with applications to quantitative nanoscopy
Johannes Schmidt-Hieber, Laura Fee Schneider, Thomas Staudt +3
Estimation of the population size from i.i.d.\ binomial observations with unknown success probability is relevant to a multitude of applications and has a long history.…