Optimal transport with some directed distances
Wolfgang Stummer
TL;DR
This paper introduces a toolkit of directed distances between quantile functions to enhance optimal transport problems, offering increased flexibility over traditional Wasserstein-based methods.
Contribution
The paper develops new directed distances between quantile functions, enabling more flexible solutions to optimal transport problems beyond Wasserstein distances.
Findings
New directed distances facilitate flexible OT solutions
Enhanced OT methods outperform traditional Wasserstein-based approaches
Toolkit broadens applicability of optimal transport techniques
Abstract
We present a toolkit of directed distances between quantile functions. By employing this, we solve some new optimal transport (OT) problems which e.g. considerably flexibilize some prominent OTs expressed through Wasserstein distances.
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