相关论文: When OT meets MoM: Robust estimation of Wasserstei…
We study the problem of robust distribution estimation under the Wasserstein distance, a popular discrepancy measure between probability distributions rooted in optimal transport (OT) theory. Given $n$ samples from an unknown distribution…
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…
We address the problem of efficiently computing Wasserstein distances for multiple pairs of distributions drawn from a meta-distribution. To this end, we propose a fast estimation method based on regressing Wasserstein distance on sliced…
Wasserstein distances are increasingly used in a wide variety of applications in machine learning. Sliced Wasserstein distances form an important subclass which may be estimated efficiently through one-dimensional sorting operations. In…
Optimal Transport (OT) metrics allow for defining discrepancies between two probability measures. Wasserstein distance is for longer the celebrated OT-distance frequently-used in the literature, which seeks probability distributions to be…
Optimal transport (OT) provides powerful tools for comparing probability measures in various types. The Wasserstein distance which arises naturally from the idea of OT is widely used in many machine learning applications. Unfortunately,…
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…
The Wasserstein distance from optimal mass transport (OMT) is a powerful mathematical tool with numerous applications that provides a natural measure of the distance between two probability distributions. Several methods to incorporate OMT…
The Wasserstein distance is a distance between two probability distributions and has recently gained increasing popularity in statistics and machine learning, owing to its attractive properties. One important approach to extending this…
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…
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…
Generative Adversarial Networks (GANs) are one of the most practical methods for learning data distributions. A popular GAN formulation is based on the use of Wasserstein distance as a metric between probability distributions.…
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…
This paper focuses on a similarity measure, known as the Wasserstein distance, with which to compare images. The Wasserstein distance results from a partial differential equation (PDE) formulation of Monge's optimal transport problem. We…
Optimal transport (OT) and the related Wasserstein metric (W) are powerful and ubiquitous tools for comparing distributions. However, computing pairwise Wasserstein distances rapidly becomes intractable as cohort size grows. An attractive…
Robust estimation is an important problem in statistics which aims at providing a reasonable estimator when the data-generating distribution lies within an appropriately defined ball around an uncontaminated distribution. Although minimax…
The Wasserstein distance received a lot of attention recently in the community of machine learning, especially for its principled way of comparing distributions. It has found numerous applications in several hard problems, such as domain…
It was shown in [6] that the Wasserstein distance is equivalent to the Mean Optimal Sub-Pattern Assignment (MOSPA) measure for empirical probability density functions. A more recent paper [7], extends on it by drawing new connections…
When a population exhibits heterogeneity, we often model it via a finite mixture: decompose it into several different but homogeneous subpopulations. Contemporary practice favors learning the mixtures by maximizing the likelihood for…
The quantum Wasserstein distance (W-distance) is a fundamental metric for quantifying the distinguishability of quantum operations, with critical applications in quantum error correction. However, computing the W-distance remains…