Related papers: Private Wasserstein Distance
Sliced Wasserstein (SW) distance has been widely used in different application scenarios since it can be scaled to a large number of supports without suffering from the curse of dimensionality. The value of sliced Wasserstein distance is…
The convergence rate in Wasserstein distance is estimated for the empirical measures of symmetric semilinear SPDEs. Unlike in the finite-dimensional case that the convergence is of algebraic order in time, in the present situation the…
Topological Data Analysis methods can be useful for classification and clustering tasks in many different fields as they can provide two dimensional persistence diagrams that summarize important information about the shape of potentially…
Many applications in machine learning involve data represented as probability distributions. The emergence of such data requires radically novel techniques to design tractable gradient flows on probability distributions over this type of…
We study a class of quadratic Wasserstein distances on spaces consisting of generalized dynamical systems on a von Neumann algebra. We emphasize how symmetry of such a Wasserstein distance arises, but also study the asymmetric case. This…
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…
In this manuscript we investigate the equivalence of Fourier-based metrics on discrete state spaces with the well-known Wasserstein distances. While the use of Fourier-based metrics in continuous state spaces is ubiquitous since its…
Optimal transport has recently proved to be a useful tool in various machine learning applications needing comparisons of probability measures. Among these, applications of distributionally robust optimization naturally involve Wasserstein…
Generalized sliced Wasserstein distance is a variant of sliced Wasserstein distance that exploits the power of non-linear projection through a given defining function to better capture the complex structures of the probability…
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…
In this paper we propose tight upper and lower bounds for the Wasserstein distance between any two {{univariate continuous distributions}} with probability densities $p_1$ and $p_2$ having nested supports. These explicit bounds are…
Wasserstein Generative Adversarial Networks (WGANs) can be used to generate realistic samples from complicated image distributions. The Wasserstein metric used in WGANs is based on a notion of distance between individual images, which…
We propose a new minimum-distance estimator for linear random coefficient models. This estimator integrates the recently advanced sliced Wasserstein distance with the nearest neighbor methods, both of which enhance computational efficiency.…
Distribution matching is central to many vision and graphics tasks, where the widely used Wasserstein distance is too costly to compute for high dimensional distributions. The Sliced Wasserstein Distance (SWD) offers a scalable alternative,…
The paper proposes a new approach to model risk measurement based on the Wasserstein distance between two probability measures. It formulates the theoretical motivation resulting from the interpretation of fictitious adversary of robust…
Safeguarding privacy in sensitive training data is paramount, particularly in the context of generative modeling. This can be achieved through either differentially private stochastic gradient descent or a differentially private metric for…
The Wasserstein barycenter has been widely studied in various fields, including natural language processing, and computer vision. However, it requires a high computational cost to solve the Wasserstein barycenter problem because the…
The Sliced-Wasserstein distance (SW) is being increasingly used in machine learning applications as an alternative to the Wasserstein distance and offers significant computational and statistical benefits. Since it is defined as an…
We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a…
Self-supervised sequential recommendation significantly improves recommendation performance by maximizing mutual information with well-designed data augmentations. However, the mutual information estimation is based on the calculation of…