Related papers: GAN Estimation of Lipschitz Optimal Transport Maps
Despite the remarkable empirical successes of Generative Adversarial Networks (GANs), the theoretical guarantees for their statistical accuracy remain rather pessimistic. In particular, the data distributions on which GANs are applied, such…
The generation of synthetic data with distributions that faithfully emulate the underlying data-generating mechanism holds paramount significance. Wasserstein Generative Adversarial Networks (WGANs) have emerged as a prominent tool for this…
We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…
We establish the validity of asymptotic limits for the general transportation problem between random i.i.d. points and their common distribution, with respect to the squared Euclidean distance cost, in any dimension larger than three.…
This paper deals with an optimization problem over a network of agents, where the cost function is the sum of the individual objectives of the agents and the constraint set is the intersection of local constraints. Most existing methods…
We study the Neural Optimal Transport (NOT) algorithm which uses the general optimal transport formulation and learns stochastic transport plans. We show that NOT with the weak quadratic cost might learn fake plans which are not optimal. To…
Path planning plays an important role in autonomous robot systems. Effective understanding of the surrounding environment and efficient generation of optimal collision-free path are both critical parts for solving path planning problem.…
We investigate the minimum cost of a wide class of combinatorial optimization problems over random bipartite geometric graphs in $\mathbb{R}^d$ where the edge cost between two points is given by a $p$-th power of their Euclidean distance.…
In many statistical settings, two types of data are available: coupled data, which preserve the joint structure among variables but are limited in size due to cost or privacy constraints, and marginal data, which are available at larger…
In this article we show how ideas, methods and results from optimal transportation can be used to study various aspects of the stationary measuresof Iterated Function Systems equipped with a probability distribution. We recover a classical…
We derive limit distributions for certain empirical regularized optimal transport distances between probability distributions supported on a finite metric space and show consistency of the (naive) bootstrap. In particular, we prove that the…
Understanding the generalization of deep neural networks is one of the most important tasks in deep learning. Although much progress has been made, theoretical error bounds still often behave disparately from empirical observations. In this…
This paper focuses on martingale optimal transport problems when the martingales are assumed to have bounded quadratic variation. First, we give a result that characterizes the existence of a probability measure satisfying some convex…
Unbalanced optimal transport (UOT) extends classical optimal transport to measures with different total masses, but statistical guarantees for Monge-type estimation remain limited. We study unbalanced transport with quadratic cost and…
Optimal Transport is a foundational mathematical theory that connects optimization, partial differential equations, and probability. It offers a powerful framework for comparing probability distributions and has recently become an important…
In this paper, we extend the scope of Caffarelli's contraction theorem, which provides a measure of the Lipschitz constant for optimal transport maps between log-concave probability densities in $\R^d$. Our focus is on a broader category of…
It is common in nonparametric estimation problems to impose a certain low-dimensional structure on the unknown parameter to avoid the curse of dimensionality. This paper considers a nonparametric distribution estimation problem with a…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Optimal transport (OT) is a versatile framework for comparing probability measures, with many applications to statistics, machine learning, and applied mathematics. However, OT distances suffer from computational and statistical scalability…
Transportation cost is an attractive similarity measure between probability distributions due to its many useful theoretical properties. However, solving optimal transport exactly can be prohibitively expensive. Therefore, there has been…