Related papers: Optimal quantization with branched optimal transpo…
We consider so-called branched transport and variants thereof in two space dimensions. In these models one seeks an optimal transportation network for a given mass transportation task. In two space dimensions, they are closely connected to…
The distance and divergence of the probability measures play a central role in statistics, machine learning, and many other related fields. The Wasserstein distance has received much attention in recent years because of its distinctions…
Graph summarization is the problem of producing smaller graph representations of an input graph dataset, in such a way that the smaller compressed graphs capture relevant structural information for downstream tasks. There is a recent graph…
This work considers the problem of computing distances between structured objects such as undirected graphs, seen as probability distributions in a specific metric space. We consider a new transportation distance (i.e. that minimizes a…
We develop criteria based on a calibration argument via discrete PDE and semidiscrete optimal transport, for finding sharp isoperimetric inequalities of the form $(\sharp \Omega)^{d-1} \le C (\sharp \overrightarrow{\partial\Omega})^d$ where…
In this paper, we study parametric analysis of semidefinite optimization problems w.r.t. the perturbation of the objective function. We study the behavior of the optimal partition and optimal set mapping on a so-called nonlinearity…
We consider a Beckmann formulation of an unbalanced optimal transport (UOT) problem. The $\Gamma$-convergence of this formulation of UOT to the corresponding optimal transport (OT) problem is established as the balancing parameter $\alpha$…
Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…
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…
In this work, we propose a novel approach for subgraph matching, the problem of finding a given query graph in a large source graph, based on the fused Gromov-Wasserstein distance. We formulate the subgraph matching problem as a partial…
This paper explores the process of optimal quantization for several types of discrete probability distributions. Quantization is a technique used to approximate a complex distribution with a smaller set of representative points, which is…
We study the quadratically regularized optimal transport (QOT) problem for quadratic cost and compactly supported marginals $\mu$ and $\nu$. It has been empirically observed that the optimal coupling $\pi_\epsilon$ for the QOT problem has…
A quantum version of the Monge--Kantorovich optimal transport problem is analyzed. The transport cost is minimized over the set of all bipartite coupling states $\rho^{AB}$, such that both of its reduced density matrices $\rho^A$ and…
We study the Kantorovich-Rubinstein transhipment problem when the difference between the source and the target is not anymore a balanced measure but belongs to a suitable subspace $X(\Omega)$ of first order distribution. A particular…
This paper develops a comprehensive theory of optimal transport for signed (real) measures on Rd. Extending the classical Brenier theorem, we consider Jordan decompositions of measures with possibly fractal singular parts. Under suitable…
We introduce a novel optimal transport framework for probabilistic circuits (PCs). While it has been shown recently that divergences between distributions represented as certain classes of PCs can be computed tractably, to the best of our…
We study the Bergman determinantal point process from a theoretical point of view motivated by its simulation. We construct restricted and restricted-truncated variants of the Bergman kernel and show optimal transport inequalities involving…
Optimal transport aims to learn a mapping of sources to targets by minimizing the cost, which is typically defined as a function of distance. The solution to this problem consists of straight line segments optimally connecting sources to…
In this work we analyze regularized optimal transport problems in the so-called Kantorovich form, i.e. given two Radon measures on two compact sets, the aim is to find a transport plan, which is another Radon measure on the product of the…
Optimal transport and Wasserstein distance are prominent tools to quantify the space of probability distributions. From a novel viewpoint of manifold hypothesis in machine learning being a possible guide for the holographic principle, we…