Related papers: Neural Wasserstein Two-Sample Tests
This paper studies the expected optimal value of a mixed 0-1 programming problem with uncertain objective coefficients following a joint distribution. We assume that the true distribution is not known exactly, but a set of independent…
This paper focuses on the Wasserstein distributionally robust mean-lower semi-absolute deviation (DR-MLSAD) model, where the ambiguity set is a Wasserstein ball centered on the empirical distribution of the training sample. This model can…
Given a cloud of $n$ data points in $\mathbb{R}^d$, consider all projections onto $m$-dimensional subspaces of $\mathbb{R}^d$ and, for each such projection, the empirical distribution of the projected points. What does this collection of…
In this work, we propose a novel generalized Wasserstein-2 distance approach for efficiently training stochastic neural networks to reconstruct random field models, where the target random variable comprises both continuous and categorical…
Computing Wasserstein barycenters of discrete measures has recently attracted considerable attention due to its wide variety of applications in data science. In general, this problem is NP-hard, calling for practical approximative…
Under mild assumptions, we show the exact convergence rate in total variation is also exact in weaker Wasserstein distances for the Metropolis-Hastings independence sampler. We develop a new upper and lower bound on the worst-case…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…
The Wasserstein distance has become increasingly important in machine learning and deep learning. Despite its popularity, the Wasserstein distance is hard to approximate because of the curse of dimensionality. A recently proposed approach…
We present a way to use Stein's method in order to bound the Wasserstein distance of order $2$ between two measures $\nu$ and $\mu$ supported on $\mathbb{R}^d$ such that $\mu$ is the reversible measure of a diffusion process. In order to…
As opposed to standard empirical risk minimization (ERM), distributionally robust optimization aims to minimize the worst-case risk over a larger ambiguity set containing the original empirical distribution of the training data. In this…
Sampling from an unknown distribution, accessible only through discrete samples, is a fundamental problem at the core of generative AI. The current state-of-the-art methods follow a two-step process: first, estimating the score function…
The empirical Wasserstein projection (WP) distance quantifies the Wasserstein distance from the empirical distribution to a set of probability measures satisfying given expectation constraints. The WP is a powerful tool because it mitigates…
Computing the infinity Wasserstein distance and retrieving projections of a probability measure onto a closed subset of probability measures are critical sub-problems in various applied fields. However, the practical applicability of these…
The Wasserstein distance is a metric on a space of probability measures that has seen a surge of applications in statistics, machine learning, and applied mathematics. However, statistical aspects of Wasserstein distances are bottlenecked…
The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…
We investigate a simple approximation scheme, based on overlapping linear decision rules, for solving data-driven two-stage distributionally robust optimization problems with the type-$\infty$ Wasserstein ambiguity set. Our main result…
Diffusion models have become the most popular approach to deep generative modeling of images, largely due to their empirical performance and reliability. From a theoretical standpoint, a number of recent works have studied the iteration…
Let $ (Z_{n})_{n\geq 0} $ be a supercritical branching process in an independent and identically distributed random environment. We establish an optimal convergence rate in the Wasserstein-$1$ distance for the process $ (Z_{n})_{n\geq 0} $,…
We develop a framework for generalized variational inference in infinite-dimensional function spaces and use it to construct a method termed Gaussian Wasserstein inference (GWI). GWI leverages the Wasserstein distance between Gaussian…