Related papers: The rival coffee shop problem
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight…
It is shown that under suitable regularity conditions, differential entropy is a Lipschitz functional on the space of distributions on $n$-dimensional Euclidean space with respect to the quadratic Wasserstein distance. Under similar…
The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for…
The prior distribution is a crucial building block in Bayesian analysis, and its choice will impact the subsequent inference. It is therefore important to have a convenient way to quantify this impact, as such a measure of prior impact will…
We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…
We propose iterative algorithms to solve adversarial problems in a variety of supervised learning settings of interest. Our algorithms, which can be interpreted as suitable ascent-descent dynamics in Wasserstein spaces, take the form of a…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have…
This paper is a continuation of our accompanying paper [Talbi, Touzi and Zhang (2021)], where we characterized the mean field optimal stopping problem by an obstacle equation on the Wasserstein space of probability measures, provided that…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
Equilibrium multi-population matching (matching for teams) is a problem from mathematical economics which is related to multi-marginal optimal transport. A special but important case is the Wasserstein barycenter problem, which has…
The Wasserstein distance quantifies the distance between two probability measures on a metric space. We prove an analogue of the Berry-Esseen inequality for the Wasserstein distance on a finite area hyperbolic surface. This inequality…
We introduce a version of Stein's method of comparison of operators specifically tailored to the problem of bounding the Wasserstein-1 distance between continuous and discrete distributions on the real line. Our approach rests on a new…
Since the introduction of the Sliced Wasserstein distance in the literature, its simplicity and efficiency have made it one of the most interesting surrogate for the Wasserstein distance in image processing and machine learning. However,…
Learning to predict multi-label outputs is challenging, but in many problems there is a natural metric on the outputs that can be used to improve predictions. In this paper we develop a loss function for multi-label learning, based on the…
In this paper, we consider contextual stochastic optimization problems under endogenous uncertainty, where decisions affect the underlying distributions. To implement such decisions in practice, it is crucial to ensure that their outcomes…
In inverse problems, many conditional generative models approximate the posterior measure by minimizing a distance between the joint measure and its learned approximation. While this approach also controls the distance between the posterior…
We study the problem of robust distribution estimation under the Wasserstein distance, a popular discrepancy measure between probability distributions rooted in optimal transport (OT) theory. Given $n$ samples from an unknown distribution…
We study the estimation and concentration on its expectation of the probability to observe data further than a specified distance from a given iid sample in a metric space. The problem extends the classical problem of estimation of the…
We provide an implementation to compute the flat metric in any dimension. The flat metric, also called dual bounded Lipschitz distance, generalizes the well-known Wasserstein distance $W_1$ to the case that the distributions are of unequal…