Section: New Results

Optimal transport meets machine learning

A. Genevay, G. Peyré, M. Cuturi, F. Bach

Optimal transport has recently proved (in particular through the works of our team) to be very successful to solve various low dimensional problems, mostly in 2-D and 3-D. These successes are mainly due to the specicfic structure of these problems (the connections with PDE's and the use of entropic regularization), but these approaches do not scale to high dimensional and large scale problems that one encounters in machine learning. In these problems, it is not possible to discretize the space, and one does not have a direct access to the density to compare. One can rather only sample from these distributions. To address these difficulties, we propose in [20] (published in NIPS, one of the best two machine learning conferences), the first provably convergent algorithm that can cope with high dimensional OT problems, with both discrete and continuous input measures. This approach leverage both the structure of the dual problem, and the smoothness induced by an entropic regularization. We show application of this method for classification of high dimensional bag of features histograms.