Related papers: Fundamental Properties of Process Distances
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…
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…
Understanding the space of probability measures on a metric space equipped with a Wasserstein distance is one of the fundamental questions in mathematical analysis. The Wasserstein metric has received a lot of attention in the machine…
Sliced Wasserstein distances preserve properties of classic Wasserstein distances while being more scalable for computation and estimation in high dimensions. The goal of this work is to quantify this scalability from three key aspects: (i)…
Statistical solutions have recently been introduced as a an alternative solution framework for hyperbolic systems of conservation laws. In this work we derive a novel a posteriori error estimate in the Wasserstein distance between…
Multi-marginal optimal transport enables one to compare multiple probability measures, which increasingly finds application in multi-task learning problems. One practical limitation of multi-marginal transport is computational scalability…
The Wasserstein distance between two probability measures on a metric space is a measure of closeness with applications in statistics, probability, and machine learning. In this work, we consider the fundamental question of how quickly the…
The squared Wasserstein distance is a natural quantity to compare probability distributions in a non-parametric setting. This quantity is usually estimated with the plug-in estimator, defined via a discrete optimal transport problem which…
Topological phases are generally characterized by topological invariants denoted by integer numbers. However, different topological systems often require different topological invariants to measure, such as geometric phases, topological…
Scientific datasets often have hierarchical structure: for example, in surveys, individual participants (samples) might be grouped at a higher level (units) such as their geographical region. In these settings, the interest is often in…
Motivated by the growing popularity of variants of the Wasserstein distance in statistics and machine learning, we study statistical inference for the Sliced Wasserstein distance--an easily computable variant of the Wasserstein distance.…
While theoretically appealing, the application of the Wasserstein distance to large-scale machine learning problems has been hampered by its prohibitive computational cost. The sliced Wasserstein distance and its variants improve the…
Modeling observations as random distributions embedded within Wasserstein spaces is becoming increasingly popular across scientific fields, as it captures the variability and geometric structure of the data more effectively. However, the…
We provide a general steady-state diffusion approximation result which bounds the Wasserstein distance between the reversible measure $\mu$ of a diffusion process and the measure $\nu$ of an approximating Markov chain. Our result is…
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…
We develop a general framework for statistical inference with the 1-Wasserstein distance. Recently, the Wasserstein distance has attracted considerable attention and has been widely applied to various machine learning tasks because of its…
We investigate properties of some extensions of a class of Fourier-based probability metrics, originally introduced to study convergence to equilibrium for the solution to the spatially homogeneous Boltzmann equation. At difference with the…
The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…
Random measures provide flexible parameters for Bayesian nonparametric models. Given two different priors for a random measure, we develop a natural framework to investigate the rate at which the corresponding posteriors merge, as the…
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…