Optimal transport (OT) theory can be informally described using the words of the French
mathematician Gaspard Monge (1746–1818): A worker with a shovel in hand has to move a …

Wasserstein distances are metrics on probability distributions inspired by the problem of
optimal mass transportation. Roughly speaking, they measure the minimal effort required to …

We are performing the digital transition of industry, living the 4th industrial revolution,
building a new World in which the digital, physical and human dimensions are interrelated in …

There is intense interest in applying machine learning to problems of causal inference in
fields such as healthcare, economics and education. In particular, individual-level causal …

Optimal transport has recently been reintroduced to the machine learning community thanks
in part to novel efficient optimization procedures allowing for medium to large scale …

Domain adaptation is one of the most challenging tasks of modern data analytics. If the
adaptation is done correctly, models built on a specific data representation become more …

We propose in this paper a differentiable learning loss between time series, building upon
the celebrated dynamic time war** (DTW) discrepancy. Unlike the Euclidean distance …

The ability to compare two degenerate probability distributions, that is two distributions
supported on low-dimensional manifolds in much higher-dimensional spaces, is a crucial …

This paper details a general numerical framework to approximate solutions to linear
programs related to optimal transport. The general idea is to introduce an entropic …

This paper introduces a new class of algorithms for optimization problems involving optimal
transportation over geometric domains. Our main contribution is to show that optimal …