Learning with minibatch Wasserstein : asymptotic and gradient properties [article]

Kilian Fatras, Younes Zine, Rémi Flamary, Rémi Gribonval, Nicolas Courty
2021 arXiv   pre-print
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 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
more » ... at 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.
arXiv:1910.04091v4 fatcat:wqdqgos4kbh7xa32lf5sefws3u