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 …

This is an expository paper on the theory of gradient flows, and in particular of those PDEs
which can be interpreted as gradient flows for the Wasserstein metric on the space of …

We propose the Wasserstein Auto-Encoder (WAE)---a new algorithm for building a
generative model of the data distribution. WAE minimizes a penalized form of the …

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 …

Abstract Multi-Source Domain Adaptation (MSDA) techniques have attracted widespread
attention due to their availability to transfer knowledge from multiple source domains to the …

Through prompting, large-scale pre-trained models have become more expressive and
powerful, gaining significant attention in recent years. Though these big models have zero …

Time-series single-cell RNA sequencing (scRNA-seq) datasets provide unprecedented
opportunities to learn dynamic processes of cellular systems. Due to the destructive nature …

This article introduces a new class of fast algorithms to approximate variational problems
involving unbalanced optimal transport. While classical optimal transport considers only …

Learning the continuous dynamics of a system from snapshots of its temporal marginals is a
problem which appears throughout natural sciences and machine learning, including in …

Scaling algorithms for entropic transport-type problems have become a very popular
numerical method, encompassing Wasserstein barycenters, multimarginal problems …