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Florian Heinemann

Publications and source records attributed to Florian Heinemann.

5 recordsLinked to original sources
arXiv2024

Unbalanced Kantorovich-Rubinstein distance, plan, and barycenter on finite spaces: A statistical perspective

We analyze statistical properties of plug-in estimators for unbalanced optimal transport quantities between finitely supported measures in different prototypical sampling models. Specifically, our main results provide non-asymptotic bounds on the expected error of empirical Kantorovich-Rubinstein (KR) distance, plans, and barycenters for mass penalty parameter $C>0$. The impact of the mass penalty parameter $C$ is studied in detail. Based on this analysis, we mathematically justify randomized computational schemes for KR quantities which can be used for fast approximate computations in combination with any exact solver. Using synthetic and real datasets, we empirically analyze the behavior of the expected errors in simulation studies and illustrate the validity of our theoretical bounds.

stat.ME↗
arXiv2022

Kantorovich-Rubinstein distance and barycenter for finitely supported measures: Foundations and Algorithms

The purpose of this paper is to provide a systematic discussion of a generalized barycenter based on a variant of unbalanced optimal transport (UOT) that defines a distance between general non-negative, finitely supported measures by allowing for mass creation and destruction modeled by some cost parameter. They are denoted as Kantorovich-Rubinstein (KR) barycenter and distance. In particular, we detail the influence of the cost parameter to structural properties of the KR barycenter and the KR distance. For the latter we highlight a closed form solution on ultra-metric trees. The support of such KR barycenters of finitely supported measures turns out to be finite in general and its structure to be explicitly specified by the support of the input measures. Additionally, we prove the existence of sparse KR barycenters and discuss potential computational approaches. The performance of the KR barycenter is compared to the OT barycenter on a multitude of synthetic datasets. We also consider barycenters based on the recently introduced Gaussian Hellinger-Kantorovich and Wasserstein-Fisher-Rao distances.

math.OC↗
arXiv2021

Randomised Wasserstein Barycenter Computation: Resampling with Statistical Guarantees

We propose a hybrid resampling method to approximate finitely supported Wasserstein barycenters on large-scale datasets, which can be combined with any exact solver. Nonasymptotic bounds on the expected error of the objective value as well as the barycenters themselves allow to calibrate computational cost and statistical accuracy. The rate of these upper bounds is shown to be optimal and independent of the underlying dimension, which appears only in the constants. Using a simple modification of the subgradient descent algorithm of Cuturi and Doucet, we showcase the applicability of our method on a myriad of simulated datasets, as well as a real-data example from cell microscopy which are out of reach for state of the art algorithms for computing Wasserstein barycenters.

stat.CO↗
arXiv2004

The discovery potential of the second-lightest neutralino in mSUGRA in the tau-channel at high tan(b) at the LHC

One of the main physics goals of the Large Hadron Collider is the search of particles predicted by supersymmetric theories. This study analyses the possibility of using kinematic endpoints of mass spectra for a sparticle mass reconstruction. It focuses on cascade decays, which include the second-lightest neutralino, in the mSUGRA framework with tan(b) = 35, A0 = 0 and positive mu. A region of 25 points around the benchmark point I' with m0 = 181 and m1/2 = 350 is chosen, where the cascade decay of the second-lightest neutralino into two opposite-sign taus and the lightest neutralino has a branching ratio of over 95%. Two methods of measuring 13 kinematic limits are tested systematically at Monte Carlo generator level.

hep-ex↗