77 citations · 561 across the 68 of their papers we have counts for
34 papers · 1 filter
Gromov-Wasserstein Barycenter Surrogates: Statistical Methodology, Distributional Limits and Applications
Florian Steinkamp, Luis-Alberto Rodríguez, Jan Victor Otte +1
We introduce statistical theory for the matching of finitely many objects, represented as metric measure spaces (mm-spaces). The approach is based on the second lower bound (SLB) o…
Empirical Optimal Transport under Estimated Costs: Distributional Limits and Statistical Applications
Shayan Hundrieser, Gilles Mordant, Christoph Alexander Weitkamp +1
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of di…
Statistical analysis of random objects via metric measure Laplacians
Gilles Mordant, Axel Munk
In this paper, we consider a certain convolutional Laplacian for metric measure spaces and investigate its potential for the statistical analysis of complex objects. The spectrum o…
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…
Minimax detection of localized signals in statistical inverse problems
Markus Pohlmann, Frank Werner, Axel Munk
We investigate minimax testing for detecting local signals or linear combinations of such signals when only indirect data is available. Naturally, in the presence of noise, signals…
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…