Related papers: Order $p$ quantum Wasserstein distances from coupl…
In this paper we introduce a Wasserstein-type distance on the set of Gaussian mixture models. This distance is defined by restricting the set of possible coupling measures in the optimal transport problem to Gaussian mixture models. We…
Wasserstein distances provide a powerful framework for comparing data distributions. They can be used to analyze processes over time or to detect inhomogeneities within data. However, simply calculating the Wasserstein distance or analyzing…
The Wasserstein distance, rooted in optimal transport (OT) theory, is a popular discrepancy measure between probability distributions with various applications to statistics and machine learning. Despite their rich structure and…
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…
The Wasserstein distance $\mathcal{W}_p$ is an important instance of an optimal transport cost. Its numerous mathematical properties as well as applications to various fields such as mathematical finance and statistics have been well…
The question of optimally approximating an arbitrary probability measure in the Wasserstein distance by a discrete one with uniform weights is considered. Estimates are obtained for the optimal approximation distance, with an explicit rate…
We are interested in the Wasserstein distance between two probability measures on $\R^n$ sharing the same copula $C$. The image of the probability measure $dC$ by the vectors of pseudo-inverses of marginal distributions is a natural…
We develop the theory of a metric, which we call the $\nu$-based Wasserstein metric and denote by $W_\nu$, on the set of probability measures $\mathcal P(X)$ on a domain $X \subseteq \mathbb{R}^m$. This metric is based on a slight…
Optimal transport and the Wasserstein distance $\mathcal{W}_p$ have recently seen a number of applications in the fields of statistics, machine learning, data science, and the physical sciences. These applications are however severely…
We introduce the observable Wasserstein distance, a framework for deriving lower bounds on the Wasserstein distance between probability measures on Polish metric spaces, designed to bypass the computational intractability of exact optimal…
Quantum Wasserstein divergences are modified versions of quantum Wasserstein distances defined by channels, and they are conjectured to be genuine metrics on quantum state spaces by De Palma and Trevisan. We prove triangle inequality for…
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.…
We investigate the stability of the Wasserstein distance, a metric structure on the space of probability measures arising from the theory of optimal transport, under metric ultralimits. We first show that if $(X_{i},d_{i})_{i\in\mathbb{N}}$…
The Wasserstein metric is an important measure of distance between probability distributions, with applications in machine learning, statistics, probability theory, and data analysis. This paper provides upper and lower bounds on…
Making sense of Wasserstein distances between discrete measures in high-dimensional settings remains a challenge. Recent work has advocated a two-step approach to improve robustness and facilitate the computation of optimal transport, using…
We consider several definitions of the quantum Wasserstein distance based on an optimization over general bipartite quantum states with given marginals. Then, we examine the quantities obtained after the optimization is carried out over…
We study the problem of minimizing the Wasserstein distance between a probability distribution and an algebraic variety. We consider the setting of finite state spaces and describe the solution depending on the choice of the ground metric…
Probability distributions play a central role in quantum mechanics, and even more so in quantum optics with its rich diversity of theoretically conceivable and experimentally accessible quantum states of light. Quantifiers that compare two…
We study the average $p-$Wasserstein distance between a finite sample of an infinite hyperuniform point process on $\mathbb{R}^2$ and its mean for any $p\geq 1$. The average Wasserstein transport cost is shown to be bounded from above and…
With the help of a given distance matrix of size $n$, we construct an infinite family of distances $d_p$ (where $p \geq 2$) on the complex projective space $\mathbb{P}(\mathbb{C}^n)$ modelling the space of pure states of an $n$-level…