Related papers: Stereographic Spherical Sliced Wasserstein Distanc…
Generalized Wasserstein distances allow to quantitatively compare two continuous or atomic mass distributions with equal or different total mass. In this paper, we propose four numerical methods for the approximation of three different…
Finding meaningful distances between high-dimensional data samples is an important scientific task. To this end, we propose a new tree-Wasserstein distance (TWD) for high-dimensional data with two key aspects. First, our TWD is specifically…
In many robotics applications, it is necessary to compute not only the distance between the robot and the environment, but also its derivative - for example, when using control barrier functions. However, since the traditional Euclidean…
Persistence diagrams, an important summary in topological data analysis, consist of a set of ordered pairs, each with positive multiplicity. Persistence diagrams are obtained via Mobius inversion and may be compared using a one-parameter…
The nested distance builds on the Wasserstein distance to quantify the difference of stochastic processes, including also the information modelled by filtrations. The Sinkhorn divergence is a relaxation of the Wasserstein distance, which…
Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…
Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown, in applications such as domain adaptation, to provide performances…
Gaussian mixture models (GMM) are powerful parametric tools with many applications in machine learning and computer vision. Expectation maximization (EM) is the most popular algorithm for estimating the GMM parameters. However, EM…
Approximate Bayesian Computation (ABC) is a popular method for approximate inference in generative models with intractable but easy-to-sample likelihood. It constructs an approximate posterior distribution by finding parameters for which…
The Wasserstein distance has emerged as a key metric to quantify distances between probability distributions, with applications in various fields, including machine learning, control theory, decision theory, and biological systems.…
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…
We study the Wasserstein metric to measure distances between molecules represented by the atom index dependent adjacency "Coulomb" matrix, used in kernel ridge regression based supervised learning. Resulting quantum machine learning models…
Monte Carlo (MC) integration has been employed as the standard approximation method for the Sliced Wasserstein (SW) distance, whose analytical expression involves an intractable expectation. However, MC integration is not optimal in terms…
We study a new class of distances between Radon measures similar to those studied in a recent paper of Dolbeault-Nazaret-Savar\'e [DNS]. These distances (more correctly pseudo-distances because can assume the value $+\infty$) are defined…
This work characterizes, analytically and numerically, two major effects of the quadratic Wasserstein ($W_2$) distance as the measure of data discrepancy in computational solutions of inverse problems. First, we show, in the…
We study the problem of quantifying how far an empirical distribution deviates from Gaussianity under the framework of optimal transport. By exploiting the cone geometry of the relative translation invariant quadratic Wasserstein space, we…
We present the Fourier Sliced-Wasserstein (FSW) embedding - a novel method to embed multisets and measures over R^d into Euclidean space. Our proposed embedding approximately preserves the sliced Wasserstein distance on distributions,…
Semi-discrete optimal transport problems, which evaluate the Wasserstein distance between a discrete and a generic (possibly non-discrete) probability measure, are believed to be computationally hard. Even though such problems are…
Motivated by the Bures distance, we introduce a new family of distances, \emph{relative translation invariant Wasserstein distances}, denoted by $RW_p$, as an extension of the classical Wasserstein distances $W_p$ for $p \in [1, +\infty)$.…
We establish quantitative comparisons between classical distances for probability distributions belonging to the class of convex probability measures. Distances include total variation distance, Wasserstein distance, Kullback-Leibler…