Related papers: Regularised optimal self-transport is approximate …
We uncover connections between maximum likelihood estimation in statistics and norm minimization over a group orbit in invariant theory. We focus on Gaussian transformation families, which include matrix normal models and Gaussian graphical…
Distributionally robust optimization has been shown to offer a principled way to regularize learning models. In this paper, we find that Tikhonov regularization is distributionally robust in an optimal transport sense (i.e., if an adversary…
We consider an extension of the Monge-Kantorovitch optimal transportation problem. The mass is transported along a continuous semimartingale, and the cost of transportation depends on the drift and the diffusion coefficients of the…
We study the consequences of the equivalence between the least gradient problem and a boundary-to-boundary optimal transport problem in two dimensions. We extend the relationship between the two problems to their respective dual problems,…
We consider the problem of finding an optimal transport plan between an absolutely continuous measure $\mu$ on $\mathcal{X} \subset \mathbb{R}^d$ and a finitely supported measure $\nu$ on $\mathbb{R}^d$ when the transport cost is the…
Gaussian mixtures are a powerful and widely used tool to model non-Gaussian estimation problems. They are able to describe measurement errors that follow arbitrary distributions and can represent ambiguity in assignment tasks like point set…
In this paper, we study optimal transportation problems for multifractal random measures. Since these measures are much less regular than optimal transportation theory requires, we introduce a new notion of transportation which is…
Finding optimal trajectories for multiple traffic demands in a congested network is a challenging task. Optimal transport theory is a principled approach that has been used successfully to study various transportation problems. Its usage is…
In machine learning and computer vision, optimal transport has had significant success in learning generative models and defining metric distances between structured and stochastic data objects, that can be cast as probability measures. The…
Brenier's theorem is a cornerstone of optimal transport that guarantees the existence of an optimal transport map $T$ between two probability distributions $P$ and $Q$ over $\mathbb{R}^d$ under certain regularity conditions. The main goal…
We study the clustering task under anisotropic Gaussian Mixture Models where the covariance matrices from different clusters are unknown and are not necessarily the identical matrix. We characterize the dependence of signal-to-noise ratios…
This paper explores the controllability and state tracking of ensembles from the perspective of optimal transport theory. Ensembles, characterized as collections of systems evolving under the same dynamics but with varying initial…
Optimal transport maps and plans between two absolutely continuous measures $\mu$ and $\nu$ can be approximated by solving semi-discrete or fully-discrete optimal transport problems. These two problems ensue from approximating $\mu$ or both…
We use the randomization idea and proof techniques from optimal transport to study optimal reinsurance problems. We start by providing conditions for a class of problems that allow us to characterize the support of optimal treaties, and…
Mixtures-of-Experts models and their maximum likelihood estimation (MLE) via the EM algorithm have been thoroughly studied in the statistics and machine learning literature. They are subject of a growing investigation in the context of…
Estimating Wasserstein distances between two high-dimensional densities suffers from the curse of dimensionality: one needs an exponential (wrt dimension) number of samples to ensure that the distance between two empirical measures 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…
In its most general form, the optimal transport problem is an infinite-dimensional optimization problem, yet certain notable instances admit closed-form solutions. We identify the common source of this tractability as \textit{symmetry} and…
Gaussian mixture models are widely used to study clustering problems. These model-based clustering methods require an accurate estimation of the unknown data density by Gaussian mixtures. In Maugis and Michel (2009), a penalized maximum…
We provide a unified treatment of a broad class of noisy structure recovery problems, known as structured normal means problems. In this setting, the goal is to identify, from a finite collection of Gaussian distributions with different…