Related papers: Learning Elastic Costs to Shape Monge Displacement…
Optimal Transport is a useful metric to compare probability distributions and to compute a pairing given a ground cost. Its entropic regularization variant (eOT) is crucial to have fast algorithms and reflect fuzzy/noisy matchings. This…
We investigate metric conditions that allow to prove existence and uniqueness of a map solving the Monge problem between two marginals in a metric (measure) space, proving two main results. Firstly, we introduce a nonsmooth version of the…
We introduce a new second order stochastic algorithm to estimate the entropically regularized optimal transport cost between two probability measures. The source measure can be arbitrary chosen, either absolutely continuous or discrete,…
The inverse optimal transport problem is to find the underlying cost function from the knowledge of optimal transport plans. While this amounts to solving a linear inverse problem, in this work we will be concerned with the nonlinear…
We study the problem of evaluating a discrete function by adaptively querying the values of its variables until the values read uniquely determine the value of the function. Reading the value of a variable is done at the expense of some…
We study multi-marginal optimal transport problems from a probabilistic graphical model perspective. We point out an elegant connection between the two when the underlying cost for optimal transport allows a graph structure. In particular,…
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…
We consider the problem to transport resources/mass while abiding by constraints on the flow through constrictions along their path between specified terminal distributions. Constrictions, conceptualized as toll stations at specified…
We consider optimal transport problems where the cost for transporting a given probability measure $\mu_0$ to another one $\mu_1$ consists of two parts: the first one measures the transportation from $\mu_0$ to an intermediate (pivot)…
In this work, we consider learning over multitask graphs, where each agent aims to estimate its own parameter vector. Although agents seek distinct objectives, collaboration among them can be beneficial in scenarios where relationships…
The optimal transport (OT) map is a geometry-driven transformation between high-dimensional probability distributions which underpins a wide range of tasks in statistics, applied probability, and machine learning. However, existing…
We explore the connection between dimensionality and communication cost in distributed learning problems. Specifically we study the problem of estimating the mean $\vec{\theta}$ of an unknown $d$ dimensional gaussian distribution in the…
Recent advances in large-scale optimal transport have greatly extended its application scenarios in machine learning. However, existing methods either not explicitly learn the transport map or do not support general cost function. In this…
We consider the Monge-Kantorovich problem between two random measuress. More precisely, given probability measures $\mathbb{P}_1,\mathbb{P}_2\in\mathcal{P}(\mathcal{P}(M))$ on the space $\mathcal{P}(M)$ of probability measures on a smooth…
We propose a new algorithm that uses an auxiliary neural network to express the potential of the optimal transport map between two data distributions. In the sequel, we use the aforementioned map to train generative networks. Unlike WGANs,…
We consider Monge-Kantorovich optimal transport problems on $\mathbb{R}^d$, $d\ge 1$, with a convex cost function given by the cumulant generating function of a probability measure. Examples include the Wasserstein-2 transport whose cost…
We investigate finding a map $g$ within a function class $G$ that minimises an Optimal Transport (OT) cost between a target measure $\nu$ and the image by $g$ of a source measure $\mu$. This is relevant when an OT map from $\mu$ to $\nu$…
We consider Kantorovich optimal transportation problem in the case where the cost function and marginal distributions continuously depend on a parameter with values in a metric space. We prove the existence of approximate optimal Monge…
Many adaptive mesh methods explicitly or implicitly use equidistribution and alignment. These principles can be considered central to mesh adaption. A Metric Tensor is the tool by which one describes the desired level of mesh anisotropy. In…
Existing motion planning methods often have two drawbacks: 1) goal configurations need to be specified by a user, and 2) only a single solution is generated under a given condition. In practice, multiple possible goal configurations exist…