Related papers: Theory and Approximate Solvers for Branched Optima…
Optimal transport (OT) has become a natural framework for guiding the probability flows. Yet, the majority of recent generative models assume trivial geometry (e.g., Euclidean) and rely on strong density-estimation assumptions, yielding…
This paper presents a multiscale approach to efficiently compute approximate optimal transport plans between point sets. It is particularly well-suited for point sets that are in high-dimensions, but are close to being intrinsically…
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…
Optimal transport (OT) is a powerful framework to compare probability measures, a fundamental task in many statistical and machine learning problems. Substantial advances have been made in designing OT variants which are either…
Multimarginal Optimal Transport (MOT) is the problem of linear programming over joint probability distributions with fixed marginals. A key issue in many applications is the complexity of solving MOT: the linear program has exponential size…
We propose a new approach to graph compression by appeal to optimal transport. The transport problem is seeded with prior information about node importance, attributes, and edges in the graph. The transport formulation can be setup for…
Optimal Transport (OT) has established itself as a robust framework for quantifying differences between distributions, with applications that span fields such as machine learning, data science, and computer vision. This paper offers a…
This paper presents a Wasserstein attraction approach for solving dynamic mass transport problems over networks. In the transport problem over networks, we start with a distribution over the set of nodes that needs to be "transported" to a…
Optimal transport (OT) finds a least cost transport plan between two probability distributions using a cost matrix defined on pairs of points. Unlike standard OT, which infers unstructured pointwise mappings, low-rank optimal transport…
Optimal transport (OT) defines a powerful framework to compare probability distributions in a geometrically faithful way. However, the practical impact of OT is still limited because of its computational burden. We propose a new class of…
This study examines the time complexities of the unbalanced optimal transport problems from an algorithmic perspective for the first time. We reveal which problems in unbalanced optimal transport can/cannot be solved efficiently.…
Optimal Transport is a popular distance metric for measuring similarity between distributions. Exact algorithms for computing Optimal Transport can be slow, which has motivated the development of approximate numerical solvers (e.g. Sinkhorn…
In this work we propose a batch version of the Greenkhorn algorithm for multimarginal regularized optimal transport problems. Our framework is general enough to cover, as particular cases, some existing algorithms like Sinkhorn and…
We study augmenting a plane Euclidean network with a segment, called a shortcut, to minimize the largest distance between any two points along the edges of the resulting network. Problems of this type have received considerable attention…
We consider the problem of maximizing the revenue raised from tolls set on the arcs of a transportation network, under the constraint that users are assigned to toll-compatible shortest paths. We first prove that this problem is strongly…
Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results…
Computing optimal transport (OT) for general high-dimensional data has been a long-standing challenge. Despite much progress, most of the efforts including neural network methods have been focused on the static formulation of the OT…
The power and flexibility of Optimal Transport (OT) have pervaded a wide spectrum of problems, including recent Machine Learning challenges such as unsupervised domain adaptation. Its essence of quantitatively relating two probability…
We introduce a simple yet effective sampling-based planner that is tailored for bottleneck pathfinding: Given an implicitly-defined cost map $\mathcal{M}:\mathbb{R}^d\rightarrow \mathbb{R}$, which assigns to every point in space a real…
Energy-based models (EBMs) are known in the Machine Learning community for decades. Since the seminal works devoted to EBMs dating back to the noughties, there have been a lot of efficient methods which solve the generative modelling…