Related papers: Optimal transport with some directed distances

We introduce an efficient framework for computing the distance between collider events using the tools of Linearized Optimal Transport (LOT). This preserves many of the advantages of the recently-introduced Energy Mover's Distance, which…

While many Machine Learning methods were developed or transposed on Riemannian manifolds to tackle data with known non Euclidean geometry, Optimal Transport (OT) methods on such spaces have not received much attention. The main OT tool on…

We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…

Despite the recent popularity of neural network-based solvers for optimal transport (OT), there is no standard quantitative way to evaluate their performance. In this paper, we address this issue for quadratic-cost transport --…

We study the discretization of generalized Wasserstein distances with nonlinear mobilities on the real line via suitable discrete metrics on the cone of N ordered particles, a setting which naturally appears in the framework of…

Optimal Transport (OT) is a mathematical framework that first emerged in the eighteenth century and has led to a plethora of methods for answering many theoretical and applied questions. The last decade has been a witness to the remarkable…

Optimal transportation theory and the related $p$-Wasserstein distance ($W_p$, $p\geq 1$) are widely-applied in statistics and machine learning. In spite of their popularity, inference based on these tools has some issues. For instance, it…

Sliced Optimal Transport (SOT) is a rapidly developing branch of optimal transport (OT) that exploits the tractability of one-dimensional OT problems. By combining tools from OT, integral geometry, and computational statistics, SOT enables…

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…

We introduce a non-quadratic generalization of the quantum mechanical optimal transport problem introduced in [De Palma and Trevisan, Ann. Henri Poincar\'e, {\bf 22} (2021), 3199-3234] where quantum channels realize the transport. Relying…

With the discovery of Wasserstein GANs, Optimal Transport (OT) has become a powerful tool for large-scale generative modeling tasks. In these tasks, OT cost is typically used as the loss for training GANs. In contrast to this approach, we…

In this paper, we apply the framework of optimal transport to the formulation of optimal design problems. By considering the Wasserstein space as a set of design variables, we associate each probability measure with a shape configuration of…

We propose a new approach to measuring the agreement between two oscillatory time series, such as seismic waveforms, and demonstrate that it can be employed effectively in inverse problems. Our approach is based on Optimal Transport theory…

We study estimators of the optimal transport (OT) map between two probability distributions. We focus on plugin estimators derived from the OT map between estimates of the underlying distributions. We develop novel stability bounds for OT…

Many variants of Optimal Transport (OT) have been developed to address its heavy computation. Among them, notably, Sliced Wasserstein (SW) is widely used for application domains by projecting the OT problem onto one-dimensional lines, and…

The adapted Wasserstein distance is a metric for quantifying distributional uncertainty and assessing the sensitivity of stochastic optimization problems on time series data. A computationally efficient alternative to it, is provided by the…

Optimal transport between classical probability distributions has been proven useful in areas such as machine learning and random combinatorial optimization. Quantum optimal transport, and the quantum Wasserstein distance as the minimal…

We discuss a new notion of distance on the space of finite and nonnegative measures which can be seen as a generalization of the well-known Kantorovich-Wasserstein distance. The new distance is based on a dynamical formulation given by an…

Causal optimal transport and adapted Wasserstein distance have applications in different fields from optimization to mathematical finance and machine learning. The goal of this article is to provide equivalent formulations of these concepts…

This contribution presents substantial computational advancements to compare measures even with varying masses. Specifically, we utilize the nonequispaced fast Fourier transform to accelerate the radial kernel convolution in unbalanced…