Related papers: Robust Wasserstein barycenter
This paper considers a security constrained dispatch problem involving generation and line contingencies in the presence of the renewable generation. The uncertainty due to renewables is modeled using joint chance-constraint and the…
Wasserstein barycenters and variance-like criteria based on the Wasserstein distance are used in many problems to analyze the homogeneity of collections of distributions and structural relationships between the observations. We propose the…
The discrete Wasserstein barycenter problem is a minimum-cost mass transport problem for a set of probability measures with finite support. In this paper, we show that finding a barycenter of sparse support is hard, even in dimension 2 and…
In this paper, a regularization of Wasserstein barycenters for random measures supported on $\mathbb{R}^{d}$ is introduced via convex penalization. The existence and uniqueness of such barycenters is first proved for a large class of…
This paper is concerned by statistical inference problems from a data set whose elements may be modeled as random probability measures such as multiple histograms or point clouds. We propose to review recent contributions in statistics on…
Given a complete Riemannian manifold $M$ with a lower Ricci curvature bound, we consider barycenters in the Wasserstein space $\mathcal{W}_2(M)$ of probability measures on $M$. We refer to them as Wasserstein barycenters, which by…
This paper considers the problem of regression over distributions, which is becoming increasingly important in machine learning. Existing approaches often ignore the geometry of the probability space or are computationally expensive. To…
In this paper, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method…
We propose a multi-class point optimization formulation based on continuous Wasserstein barycenters. Our formulation is designed to handle hundreds to thousands of optimization objectives and comes with a practical optimization scheme. We…
Wasserstein distributionally robust estimators have emerged as powerful models for prediction and decision-making under uncertainty. These estimators provide attractive generalization guarantees: the robust objective obtained from the…
We study the decentralized distributed computation of discrete approximations for the regularized Wasserstein barycenter of a finite set of continuous probability measures distributedly stored over a network. We assume there is a network of…
Entropy regularization in optimal transport (OT) has been the driver of many recent interests for Wasserstein metrics and barycenters in machine learning. It allows to keep the appealing geometrical properties of the unregularized…
Optimal transport (OT)-based methods have a wide range of applications and have attracted a tremendous amount of attention in recent years. However, most of the computational approaches of OT do not learn the underlying transport map.…
We prove quantitative stability estimates for Wasserstein barycenters on Alexandrov spaces with curvature bounded from below. The proof combines the variational strategy of Carlier--Delalande--M\'erigot with heat-kernel regularization,…
In this article we study a variational problem providing a way to extend for all times minimizing geodesics connecting two given probability measures, in the Wasserstein space. This is simply obtained by allowing for negative coefficients…
Wasserstein distributionally robust control (WDRC) is an effective method for addressing inaccurate distribution information about disturbances in stochastic systems. It provides various salient features, such as an out-of-sample…
In the realm of maritime transportation, autonomous vessel navigation in natural inland waterways faces persistent challenges due to unpredictable natural factors. Existing scheduling algorithms fall short in handling these uncertainties,…
We consider a distributionally robust second-order stochastic dominance constrained optimization problem. We require the dominance constraints hold with respect to all probability distributions in a Wasserstein ball centered at the…
Motivated by the Bures distance, we introduce a new family of distances, \emph{relative translation invariant Wasserstein distances}, denoted by $RW_p$, as an extension of the classical Wasserstein distances $W_p$ for $p \in [1, +\infty)$.…
Projecting the distance measures onto a low-dimensional space is an efficient way of mitigating the curse of dimensionality in the classical Wasserstein distance using optimal transport. The obtained maximized distance is referred to as…