Necessary Condition for Rectifiability Involving Wasserstein Distance W2

A Necessary Condition for Weyl-Heisenberg Frames

Wasserstein Distance Measure Machines

This paper presents a distance-based discriminative framework for learning with probability distributions. Instead of using kernel mean embeddings or generalized radial basis kernels, we introduce embeddings based on dissimilarity of distributions to some reference distributions denoted as templates. Our framework extends the theory of similarity of Balcan et al. (2008) to the population distri...

Necessary optimality conditions for geodesics in weighted Wasserstein spaces

Abstract: The geodesic problem in Wasserstein spaces with a metric perturbed by a conformal factor is considered, and necessary optimality conditions are estabilished in a case where this conformal factor favours the spreading of the probability measure along the curve. These conditions have the form of a system of PDEs of the kind of the compressible Euler equations. Moreover, self-similar sol...

A necessary condition for multiple objective fractional programming

In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

The Gromov-Wasserstein Distance: A Brief Overview

We recall the construction of the Gromov–Wasserstein distance and concentrate on quantitative aspects of the definition.