Related papers: Linearized Optimal Transport for Collider Events
Two areas of mathematics which have received substantial attention in recent years are the theory of optimal transport and the Elliott classification programme for C*-algebras. We combine these two seemingly unrelated disciplines to make…
Freight consolidation has significant potential to reduce transportation costs and mitigate congestion and pollution. An effective load consolidation plan relies on carefully chosen consolidation points to ensure alignment with existing…
Training data are usually limited or heterogeneous in many chemical and biological applications. Existing machine learning models for chemistry and materials science fail to consider generalizing beyond training domains. In this article, we…
Transport systems on networks are crucial in various applications, but face a significant risk of being adversely affected by unforeseen circumstances such as disasters. The application of entropy-regularized optimal transport (OT) on graph…
The optimal transport (OT) problem aims to find the most efficient mapping between two probability distributions under a given cost function, and has diverse applications in many fields such as machine learning, computer vision and computer…
Optimal transport aligns samples across distributions by minimizing the transportation cost between them, e.g., the geometric distances. Yet, it ignores coherence structure in the data such as clusters, does not handle outliers well, and…
Many problems in machine learning involve calculating correspondences between sets of objects, such as point clouds or images. Discrete optimal transport provides a natural and successful approach to such tasks whenever the two sets of…
We derive distributional limits for empirical transport distances between probability measures supported on countable sets. Our approach is based on sensitivity analysis of optimal values of infinite dimensional mathematical programs and a…
Recently, the statistical properties of empirical Entropic Optimal Transport (EOT) have attracted great interest, as this quantity has been shown to be useful for complex data analysis, among other reasons due to its computational…
This work establishes a framework for solving inverse boundary problems with the geodesic based quadratic Wasserstein distance ($W_{2}$). A general form of the Fr\'echet gradient is systematically derived by optimal transportation (OT)…
Efficient motion planning algorithms are essential in robotics. Optimizing essential parameters, such as batch size and nearest neighbor selection in sampling-based methods, can enhance performance in the planning process. However, existing…
Optimal Transport (OT) problems arise in a wide range of applications, from physics to economics. Getting numerical approximate solution of these problems is a challenging issue of practical importance. In this work, we investigate the…
Entropic optimal transport (EOT) in continuous spaces with quadratic cost is a classical tool for solving the domain translation problem. In practice, recent approaches optimize a weak dual EOT objective depending on a single potential, but…
Efficient computation of the optimal transport distance between two distributions serves as an algorithm subroutine that empowers various applications. This paper develops a scalable first-order optimization-based method that computes…
Most autonomous vehicles rely on accurate and efficient localization, which is achieved by comparing live sensor data to a preexisting map, to navigate their environment. Balancing the accuracy of localization with computational efficiency…
Under the prevalent potential outcome model in causal inference, each unit is associated with multiple potential outcomes but at most one of which is observed, leading to many causal quantities being only partially identified. The inherent…
In the regime of bounded transportation costs, additive approximations for the optimal transport problem are reduced (rather simply) to relative approximations for positive linear programs, resulting in faster additive approximation…
The collision avoidance constraints are prominent as non-convex, non-differentiable, and challenging when defined in optimization-based motion planning problems. To overcome these issues, this paper presents a novel non-conservative…
Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling…
Optimal transport between graphs, based on Gromov-Wasserstein and other extensions, is a powerful tool for comparing and aligning graph structures. However, solving the associated non-convex optimization problems is computationally…