Learning with minibatch Wasserstein : asymptotic and gradient properties

Understand

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.