Year: 2019
Type: preprint
Abstract: Optimal transport distances are powerful tools to compare probability distributions and have found many applications in machine learning. Yet their algorithmic complexity prevents their direct use on large scale datasets. To overcome this challenge, practitioners compute these distances on minibatches {\em i.e.} they average the outcome of several smaller optimal transport problems. We propose in this paper an analysis of this practice, which effects are not well understood so far. We notably argue that it is equivalent to an implicit regularization of the original problem, with appealing properties such as unbiased estimators, gradients and a concentration bound around the expectation, but also with defects such as loss of distance property. Along with this theoretical analysis, we also conduct empirical experiments on gradient flows, GANs or color transfer that highlight the practical interest of this strategy.
Source: arXiv (Cornell University)
Institutions: Centre National de la Recherche Scientifique, Institut de Recherche en Informatique et Systèmes Aléatoires, Institut national de recherche en sciences et technologies du numérique, Université de Rennes, Laboratoire d'Informatique, du Traitement de l'Information et des Systèmes, Lagrange Laboratory, Observatoire de la Côte d’Azur, École Normale Supérieure de Lyon, Laboratoire de l'Informatique du Parallélisme
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Agence Nationale de la Recherche
OpenAlex ID: W2979482469