Related papers: Entropy-regularized optimal transport over network…
The problem of determining the joint probability distributions for correlated random variables with pre-specified marginals is considered. When the joint distribution satisfying all the required conditions is not unique, the "most unbiased"…
Optimal transport is a framework that facilitates the most efficient allocation of a limited amount of resources. However, the most efficient allocation scheme does not necessarily preserve the most fairness. In this paper, we establish a…
We establish weak limits for the empirical entropy regularized optimal transport cost, the expectation of the empirical plan and the conditional expectation. Our results require only uniform boundedness of the cost function and no…
The capacity (or maximum flow) of an unicast network is known to be equal to the minimum s-t cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is dynamically changing or unknown, it is not…
We consider the problem of estimating the optimal transport map between two probability distributions, $P$ and $Q$ in $\mathbb R^d$, on the basis of i.i.d. samples. All existing statistical analyses of this problem require the assumption…
In many applications of optimal transport (OT), the object of primary interest is the optimal transport map. This map rearranges mass from one probability distribution to another in the most efficient way possible by minimizing a specified…
Many situations in physics, biology, and engineering consist of the transport of some physical quantity through a network of narrow channels. The ability of a network to transport such a quantity in every direction can be described by the…
Given a discrete source distribution $\mu$ and discrete target distribution $\nu$ on a common finite state space $\mathcal{X}$, we are tasked with transporting $\mu$ to $\nu$ using a given discrete-time Markov chain $X$ with the quickest…
Traffic dynamics is universally crucial in analyzing and designing almost any network. This article introduces a novel theoretical approach to analyzing network traffic dynamics. This theory's machinery is based on the notion of traffic…
Deterministic equilibrium flows in transport networks can be investigated by means of Markov's processes defined on the dual graph representations of the network. Sustained movement patterns are generated by a subset of automorphisms of the…
In this work, we propose a novel machine learning approach to compute the optimal transport map between two continuous distributions from their unpaired samples, based on the DeepParticle methods. The proposed method leads to a min-min…
Inspired by studies on the airports' network and the physical Internet, we propose a general model of weighted networks via an optimization principle. The topology of the optimal network turns out to be a spanning tree that minimizes a…
We introduce a constrained optimal transport problem where origins $x$ can only be transported to destinations $y\geq x$. Our statistical motivation is to describe the sharp upper bound for the variance of the treatment effect $Y-X$ given…
This paper introduces a dynamic formulation of divergence-regularized optimal transport with weak targets on the path space. In our formulation, the classical relative entropy penalty is replaced by a general convex divergence, and terminal…
We study the small-regularisation limit of the entropic optimal transport problem on the line with distance cost. While convergence of entropic minimizers is well understood in the discrete setting and in the case where the cost is…
Inspired by the matching of supply to demand in logistical problems, the optimal transport (or Monge--Kantorovich) problem involves the matching of probability distributions defined over a geometric domain such as a surface or manifold. In…
Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…
Maximization of the entropy rate is an important issue to design diffusion processes aiming at a well-mixed state. We demonstrate that it is possible to construct maximal-entropy random walks with only local information on the graph…
The congestion formation on a urban road network is one of the key issue for the development of a sustainable mobility in the future smart cities. In this work we propose a reductionist approach studying the stationary states of a simple…
The stability of optimal transport maps with respect to perturbations of the marginals is a question of interest for several reasons, ranging from the justification of the linearized optimal transport framework to numerical analysis and…