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 …

Many decision problems in science, engineering, and economics are affected by uncertain
parameters whose distribution is only indirectly observable through samples. The goal of …

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 …

We show that several machine learning estimators, including square-root least absolute
shrinkage and selection and regularized logistic regression, can be represented as …

This paper presents a new technique for computing the barycenter of a set of distance or
kernel matrices. These matrices, which define the inter-relationships between points …

This paper presents a novel two-step approach for the fundamental problem of learning an
optimal map from one distribution to another. First, we learn an optimal transport (OT) plan …

In 1931--1932, Erwin Schrödinger studied a hot gas Gedankenexperiment (an instance of
large deviations of the empirical distribution). Schrödinger's problem represents an early …

With the development of measurement technology, non-contact high-definition
measurement (HDM) systems have allowed rapid collection of large-scale point cloud data …

We present RigNet, an end-to-end automated method for producing animation rigs from
input character models. Given an input 3D model representing an articulated character …

Many shape and image processing tools rely on computation of correspondences between
geometric domains. Efficient methods that stably extract" soft" matches in the presence of …