Related papers: Geometrical Insights for Implicit Generative Model…
We propose a methodology for intercomparing climate models and evaluating their performance against benchmarks based on the use of the Wasserstein distance (WD). This distance provides a rigorous way to measure quantitatively the difference…
One of the main challenges in the parametrization of geological models is the ability to capture complex geological structures often observed in the subsurface. In recent years, generative adversarial networks (GAN) were proposed as an…
Given any deep fully connected neural network, initialized with random Gaussian parameters, we bound from above the quadratic Wasserstein distance between its output distribution and a suitable Gaussian process. Our explicit inequalities…
We study the implicit bias of generic optimization methods, such as mirror descent, natural gradient descent, and steepest descent with respect to different potentials and norms, when optimizing underdetermined linear regression or…
Wasserstein barycenters have become popular due to their ability to represent the average of probability measures in a geometrically meaningful way. In this paper, we present an algorithm to approximate the Wasserstein-2 barycenters of…
We propose conditional flows of the maximum mean discrepancy (MMD) with the negative distance kernel for posterior sampling and conditional generative modeling. This MMD, which is also known as energy distance, has several advantageous…
Recently, Deng et al. (2026) proposed Generative Modeling via Drifting (GMD), a novel framework for generative tasks. This note presents an analysis of GMD through the lens of Wasserstein Gradient Flows (WGF), i.e., the path of steepest…
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…
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…
Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…
This work presents several expected generalization error bounds based on the Wasserstein distance. More specifically, it introduces full-dataset, single-letter, and random-subset bounds, and their analogues in the randomized subsample…
We study the interaction between entropy and Wasserstein distance in free probability theory. In particular, we give lower bounds for several versions of free entropy dimension along Wasserstein geodesics, as well as study their topological…
We develop a projected Wasserstein distance for the two-sample test, a fundamental problem in statistics and machine learning: given two sets of samples, to determine whether they are from the same distribution. In particular, we aim to…
Distances between probability distributions that take into account the geometry of their sample space,like the Wasserstein or the Maximum Mean Discrepancy (MMD) distances have received a lot of attention in machine learning as they can, for…
We study a class of optimization problems in the Wasserstein space (the space of probability measures) where the objective function is nonconvex along generalized geodesics. Specifically, the objective exhibits some difference-of-convex…
The use of optimal transport cost for learning generative models has become popular with Wasserstein Generative Adversarial Networks (WGAN). Training of WGAN relies on a theoretical background: the calculation of the gradient of the optimal…
A generalization of the Wasserstein metric, the integrated transportation distance, establishes a novel distance between probability kernels of Markov systems. This metric serves as the foundation for an efficient approximation technique,…
The Wasserstein probability metric has received much attention from the machine learning community. Unlike the Kullback-Leibler divergence, which strictly measures change in probability, the Wasserstein metric reflects the underlying…
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…
Defining meaningful distances between samples in a dataset is a fundamental problem in machine learning. Optimal Transport (OT) lifts a distance between features (the "ground metric") to a geometrically meaningful distance between samples.…