Related papers: Optimal quantization with branched optimal transpo…
We consider the simultaneous optimal transportation of measures, where the target marginal is not necessarily fixed. For this problem, we prove the existence of a solution for completely regular spaces and investigate the structure of the…
We develop a theory for image restoration with a learned regularizer that is analogous to that of Meyer's characterization of solutions of the classical variational method of Rudin-Osher-Fatemi (ROF). The learned regularizer we use is a…
The modeling of phenomenological structure is a crucial aspect in inverse imaging problems. One emerging modeling tool in computational imaging is the optimal transport framework. Its ability to model geometric displacements across an…
We introduce the optimal transportation interpretation of the Kantorovich norm on thespace of signed Radon measures with finite mass, based on a generalized Wasserstein distancefor measures with different masses.With the formulation and the…
Optimal transport provides a metric which quantifies the dissimilarity between probability measures. For measures supported in discrete metric spaces, finding the optimal transport distance has cubic time complexity in the size of the…
The branched transport problem, a popular recent variant of optimal transport, is a non-convex and non-smooth variational problem on Radon measures. The so-called urban planning problem, on the contrary, is a shape optimization problem that…
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…
We consider a branched transport type problem which describes the magnetic flux through type-I superconductors in a regime of very weak applied fields. At the boundary of the sample, deviation of the magnetization from being uniform is…
We introduce a new paradigm, $\textit{measure synchronization}$, for synchronizing graphs with measure-valued edges. We formulate this problem as maximization of the cycle-consistency in the space of probability measures over relative…
We consider random i.i.d. samples of absolutely continuous measures on bounded connected domains. We prove an upper bound on the $\infty$-transportation distance between the measure and the empirical measure of the sample. The bound is…
We establish a Zador like theorem for $L^r$-optimal vector quantization when the similarity measure is a twice differentiable Bregman divergence of a strictly convex function. On our way we also prove a similar result when the Bregman…
Multi-marginal optimal transport (MOT) is a generalization of optimal transport to multiple marginals. Optimal transport has evolved into an important tool in many machine learning applications, and its multi-marginal extension opens up for…
We introduce the setting of extended metric-topological measure spaces as a general "Wiener-like" framework for optimal transport problems and nonsmooth metric analysis in infinite dimension. After a brief review of optimal transport tools…
The group of diffeomorphisms of a compact manifold endowed with the L^2 metric acting on the space of probability densities gives a unifying framework for the incompressible Euler equation and the theory of optimal mass transport. Recently,…
An optimal transport path may be viewed as a geodesic in the space of probability measures under a suitable family of metrics. This geodesic may exhibit a tree-shaped branching structure in many applications such as trees, blood vessels,…
In this paper, we provide a rigorous quantum mechanical derivation for the coherent photon transport characteristics of a two-level atom coupled to a waveguide without linearizing the coupling coefficient between the light and the atom. We…
In this paper, we present a neural network approach to address the dynamic unbalanced optimal transport problem on surfaces with point cloud representation. For surfaces with point cloud representation, traditional method is difficult to…
This paper considers estimation and inference in semiparametric econometric models. Standard procedures estimate the model based on an independence restriction that induces a minimum distance between a joint cumulative distribution function…
Optimal transport provides an inherently geometric and highly structured framework for studying spaces of probability measures, supplying a rich theoretical toolkit for contemporary statistics, machine learning, and generative modelling. In…
Classical optimal transport problem seeks a transportation map that preserves the total mass betwenn two probability distributions, requiring their mass to be the same. This may be too restrictive in certain applications such as color or…