Related papers: Data representation with optimal transport
This work is about the use of regularized optimal-transport distances for convex, histogram-based image segmentation. In the considered framework, fixed exemplar histograms define a prior on the statistical features of the two regions in…
Optimal transportation distances are valuable for comparing and analyzing probability distributions, but larger-scale computational techniques for the theoretically favorable quadratic case are limited to smooth domains or regularized…
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…
We lay out the phenomenological behavior of event-shape observables evaluated by solving optimal transport problems between collider events and reference geometries -- which we name 'manifold distances' -- to provide guidance regarding…
Distributional data have become increasingly prominent in modern signal processing, highlighting the necessity of computing optimal transport (OT) maps across multiple probability distributions. Nevertheless, recent studies on neural OT…
This paper introduces the use of unbalanced optimal transport methods as a similarity measure for diffeomorphic matching of imaging data. The similarity measure is a key object in diffeomorphic registration methods that, together with the…
Optimal transport and its related problems, including optimal partial transport, have proven to be valuable tools in machine learning for computing meaningful distances between probability or positive measures. This success has led to a…
A general class of unidirectional transforms is presented that can be computed in a distributed manner along an arbitrary routing tree. Additionally, we provide a set of conditions under which these transforms are invertible. These…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
Optimal transport (OT) has an important role in transforming data distributions in a manner which engenders fairness. Typically, the OT operators are learnt from the unfair attribute-labelled data, and then used for their repair. Two…
Optimal mass transport, also known as the earth mover's problem, is an optimization problem with important applications in various disciplines, including economics, probability theory, fluid dynamics, cosmology and geophysics to cite a few.…
The purpose of this note is to show how simple Optimal Transport arguments, on the real line, can be used in Superconcentration theory. This methodology is efficient to produce sharp non-asymptotic variance bounds for various functionals…
Optimal transport (OT) based data analysis is often faced with the issue that the underlying cost function is (partially) unknown. This paper is concerned with the derivation of distributional limits for the empirical OT value when the cost…
This paper proposes various nonparametric tools based on measure transportation for directional data. We use optimal transports to define new notions of distribution and quantile functions on the hypersphere, with meaningful quantile…
Motivated by optimal re-balancing of a portfolio, we formalize an optimal transport problem in which the transported mass is scaled by a mass-change factor depending on the source and destination. This allows direct modeling of the creation…
To remedy the drawbacks of full-mass or fixed-mass constraints in classical optimal transport, we propose adaptive optimal transport which is distinctive from the classical optimal transport in its ability of adaptive-mass preserving. It…
We address the problem of optimal transport with a quadratic cost functional and a constraint on the flux through a constriction along the path. The constriction, conceptually represented by a toll station, limits the flow rate across. We…
Modeling traffic distribution and extracting optimal flows in multilayer networks is of utmost importance to design efficient multi-modal network infrastructures. Recent results based on optimal transport theory provide powerful and…
Many causal and structural parameters in economics can be identified and estimated by computing the value of an optimization program over all distributions consistent with the model and the data. Existing tools apply when the data is…
This article studies problems of optimal transport, by embedding them in a general functional analytic framework of convex optimization. This provides a unified treatment of a large class of related problems in probability theory and allows…