Related papers: Generalized Wasserstein distance and its applicati…
Composite quantile regression has been used to obtain robust estimators of regression coefficients in linear models with good statistical efficiency. By revealing an intrinsic link between the composite quantile regression loss function and…
We investigate the Wasserstein distance between the empirical spectral distribution of non-Hermitian random matrices and the Circular Law. For general entry distributions, we obtain a nearly optimal rate of convergence in 1-Wasserstein…
We propose a generalization of the Wasserstein distance of order 1 to quantum spin systems on the lattice $\mathbb{Z}^d$, which we call specific quantum $W_1$ distance. The proposal is based on the $W_1$ distance for qudits of [De Palma et…
The Wasserstein distance has been an attractive tool in many fields. But due to its high computational complexity and the phenomenon of the curse of dimensionality in empirical estimation, various extensions of the Wasserstein distance have…
Generative Adversarial Networks (GANs) have been used to model the underlying probability distribution of sample based datasets. GANs are notoriuos for training difficulties and their dependence on arbitrary hyperparameters. One recent…
We establish novel quantitative stability results for optimal transport problems with respect to perturbations in the target measure. We provide explicit bounds on the stability of optimal transport potentials and maps, which are relevant…
This paper studies the problem of computing a linear approximation of quadratic Wasserstein distance $W_2$. In particular, we compute an approximation of the negative homogeneous weighted Sobolev norm whose connection to Wasserstein…
The curvature-dimension condition is a generalization of the Bochner inequality to weighted Riemannian manifolds and general metric measure spaces. It is now known to be equivalent to evolution variational inequalities for the heat…
Wasserstein barycenters correspond to optimal solutions of transportation problems for several marginals, and as such have a wide range of applications ranging from economics to statistics and computer science. When the marginal probability…
Measuring the distance between ontological elements is fundamental for ontology matching. String-based distance metrics are notorious for shallow syntactic matching. In this exploratory study, we investigate Wasserstein distance targeting…
In recent work arXiv:2109.07820 we have shown the equivalence of the widely used nonconvex (generalized) branched transport problem with a shape optimization problem of a street or railroad network, known as (generalized) urban planning…
In this work we analyse a number of variants of the Wasserstein distance which allow to focus the classification on the prescribed parts (fragments) of classified 2D curves. These variants are based on the use of a number of discrete…
In this paper we discuss the Wasserstein distance between the n-point motions of Harris flows whose covariance functions have compact support. We prove that it can be estimated by the diameters of their support provided the latter are…
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on…
In this work we test Wasserstein distance in conjunction with persistent homology, as a tool for discriminating large scale structures of simulated universes with different values of $\sigma_8$ cosmological parameter (present…
It is well known that nonlinear diffusion equations can be interpreted as a gradient flow in the space of probability measures equipped with the Euclidean Wasserstein distance. Under suitable convexity conditions on the nonlinearity, due to…
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…
Transport based distances, such as the Wasserstein distance and earth mover's distance, have been shown to be an effective tool in signal and image analysis. The success of transport based distances is in part due to their Lagrangian nature…
Wasserstein distance is a key metric for quantifying data divergence from a distributional perspective. However, its application in privacy-sensitive environments, where direct sharing of raw data is prohibited, presents significant…
We investigate long-time behaviors of empirical measures associated with subordinated Dirichlet diffusion processes on a compact Riemannian manifold $M$ with boundary $\partial M$ to some reference measure, under the quadratic Wasserstein…