Related papers: DOTmark - A Benchmark for Discrete Optimal Transpo…
In this work, we develop methods for few-shot image classification from a new perspective of optimal matching between image regions. We employ the Earth Mover's Distance (EMD) as a metric to compute a structural distance between dense image…
For two multisets $S$ and $T$ of points in $[\Delta]^2$, such that $|S| = |T|= n$, the earth-mover distance (EMD) between $S$ and $T$ is the minimum cost of a perfect bipartite matching with edges between points in $S$ and $T$, i.e.,…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
Distributed distribution comparison aims to measure the distance between the distributions whose data are scattered across different agents in a distributed system and cannot even be shared directly among the agents. In this study, we…
Metro networks serve as good examples of traffic systems for understanding the relations between geometric structures and transport properties.We study and compare 28 world major metro networks in terms of the Wasserstein distance, the key…
This paper proposes a data-driven distributionally robust shortest path (DRSP) model where the distribution of the travel time in the transportation network can only be partially observed through a finite number of samples. Specifically, we…
Optimal transport is widely used to learn distributions, enforce distributional constraints, and model uncertainty. In applications, transport losses are often computed from samples through tractable representations, such as one-dimensional…
We define a novel class of distances between statistical multivariate distributions by modeling an optimal transport problem on their marginals with respect to a ground distance defined on their conditionals. These new distances are metrics…
The diffusive transport distance, a novel pseudo-metric between probability measures on the real line, is introduced. It generalizes Martingale optimal transport, and forms a hierarchy with the Hellinger and the Wasserstein metrics. We…
Measuring the semantic similarity between two sentences is still an important task. The word mover's distance (WMD) computes the similarity via the optimal alignment between the sets of word embeddings. However, WMD does not utilize word…
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…
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…
A common feature of methods for analyzing samples of probability density functions is that they respect the geometry inherent to the space of densities. Once a metric is specified for this space, the Fr\'echet mean is typically used to…
Wasserstein Discriminant Analysis (WDA) is a new supervised method that can improve classification of high-dimensional data by computing a suitable linear map onto a lower dimensional subspace. Following the blueprint of classical Linear…
The optimal transport (OT) problem has gained significant traction in modern machine learning for its ability to: (1) provide versatile metrics, such as Wasserstein distances and their variants, and (2) determine optimal couplings between…
We develop a discrete optimal transport framework for analyzing simulated annealing algorithms on finite state spaces. Building on the discrete Wasserstein metric introduced by Maas (J. Funct. Anal., 2011), we define a generalized discrete…
A novel framework for density estimation under expectation constraints is proposed. The framework minimizes the Wasserstein distance between the estimated density and a prior, subject to the constraints that the expected value of a set of…
Measuring dependence between random variables is a fundamental problem in Statistics, with applications across diverse fields. While classical measures such as Pearson's correlation have been widely used for over a century, they have…
Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport…
Optimal transport induces the Earth Mover's (Wasserstein) distance between probability distributions, a geometric divergence that is relevant to a wide range of problems. Over the last decade, two relaxations of optimal transport have been…