Related papers: Wasserstein GANs are Minimax Optimal Distribution …
We are interested in the approximation in Wasserstein distance with index $\rho\ge 1$ of a probability measure $\mu$ on the real line with finite moment of order $\rho$ by the empirical measure of $N$ deterministic points. The minimal error…
Flow Matching has recently gained attention in generative modeling as a simple and flexible alternative to diffusion models. While existing statistical guarantees adapt tools from the analysis of diffusion models, we take a different…
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…
The unequal representation of different groups in a sample population can lead to discrimination of minority groups when machine learning models make automated decisions. To address these issues, fairness-aware machine learning jointly…
We study policy gradient methods for continuous-action, entropy-regularized reinforcement learning through the lens of Wasserstein geometry. Starting from a Wasserstein proximal update, we derive Wasserstein Proximal Policy Gradient (WPPG)…
GANs excel at learning high dimensional distributions, but they can update generator parameters in directions that do not correspond to the steepest descent direction of the objective. Prominent examples of problematic update directions…
Generative adversarial networks (GANs) are powerful generative models, but usually suffer from instability and generalization problem which may lead to poor generations. Most existing works focus on stabilizing the training of the…
For $\ell\colon \mathbb{R}^d \to [0,\infty)$ we consider the sequence of probability measures $\left(\mu_n\right)_{n \in \mathbb{N}}$, where $\mu_n$ is determined by a density that is proportional to $\exp(-n\ell)$. We allow for infinitely…
Let $\pi\in \Pi(\mu,\nu)$ be a coupling between two probability measures $\mu$ and $\nu$ on a Polish space. In this article we propose and study a class of nonparametric measures of association between $\mu$ and $\nu$, which we call…
In this paper, we investigate the underlying factor that leads to failure and success in the training of GANs. We study the property of the optimal discriminative function and show that in many GANs, the gradient from the optimal…
We propose a new formulation and learning strategy for computing the Wasserstein geodesic between two probability distributions in high dimensions. By applying the method of Lagrange multipliers to the dynamic formulation of the optimal…
We provide upper bounds of the expected Wasserstein distance between a probability measure and its empirical version, generalizing recent results for finite dimensional Euclidean spaces and bounded functional spaces. Such a generalization…
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…
We develop a discrete optimal transport framework for analyzing simulated annealing algorithms on finite state spaces. Building on the discrete Wasserstein metric introduced by Maas (J. Funct. Anal., 2011), we define a generalized discrete…
Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…
In the recent years Generative Adversarial Networks (GANs) have demonstrated significant progress in generating authentic looking data. In this work we introduce our simple method to exploit the advancements in well established image-based…
Semi-supervision in Machine Learning can be used in searches for new physics where the signal plus background regions are not labelled. This strongly reduces model dependency in the search for signals Beyond the Standard Model. This…
We propose a new method for smoothly interpolating probability measures using the geometry of optimal transport. To that end, we reduce this problem to the classical Euclidean setting, allowing us to directly leverage the extensive toolbox…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…
We study the convergence rate of the optimal quantization for a probability measure sequence $(\mu_{n})_{n\in\mathbb{N}^{*}}$ on $\mathbb{R}^{d}$ converging in the Wasserstein distance in two aspects: the first one is the convergence rate…