相关论文: On Barycenter Computation: Semi-Unbalanced Optimal…
We study first-order optimization algorithms for computing the barycenter of Gaussian distributions with respect to the optimal transport metric. Although the objective is geodesically non-convex, Riemannian GD empirically converges…
The optimal transportation problem defines a geometry of probability measures which leads to a definition for weighted averages (barycenters) of measures, finding application in the machine learning and computer vision communities as a…
Wasserstein barycenters provide a geometrically meaningful way to aggregate probability distributions, built on the theory of optimal transport. They are difficult to compute in practice, however, leading previous work to restrict their…
We explore the geometry of the Bures-Wasserstein space for potentially degenerate Gaussian measures on a separable Hilbert space. In this general setting, the optimal transport map is formally the subgradient of a convex function that is…
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.…
Aggregating data from multiple sources can be formalized as an Optimal Transport (OT) barycenter problem, which seeks to compute the average of probability distributions with respect to OT discrepancies. However, in real-world scenarios,…
The optimal transport barycenter (a.k.a. Wasserstein barycenter) is a fundamental notion of averaging that extends from the Euclidean space to the Wasserstein space of probability distributions. Computation of the unregularized barycenter…
Computing the unregularized Wasserstein barycenter for measure-valued data is a challenging optimization task. Recent algorithms have been tailored to either discrete measures as point clouds or continuous measures discretized on regular…
Computationally solving multi-marginal optimal transport (MOT) with squared Euclidean costs for $N$ discrete probability measures has recently attracted considerable attention, in part because of the correspondence of its solutions with…
This paper introduces a new constraint-free concave dual formulation for the Wasserstein barycenter. Tailoring the vanilla dual gradient ascent algorithm to the Sobolev geometry, we derive a scalable Sobolev gradient ascent (SGA) algorithm…
We investigate barycenters of Gaussian process laws in adapted Wasserstein space. The adapted Wasserstein distance refines classical optimal transport by enforcing compatibility of transport plans with the temporal flow of information, and…
We present new algorithms to compute the mean of a set of empirical probability measures under the optimal transport metric. This mean, known as the Wasserstein barycenter, is the measure that minimizes the sum of its Wasserstein distances…
Given a collection of probability measures, a practitioner sometimes needs to find an "average" distribution which adequately aggregates reference distributions. A theoretically appealing notion of such an average is the Wasserstein…
Optimal transport is a notoriously difficult problem to solve numerically, with current approaches often remaining intractable for very large scale applications such as those encountered in machine learning. Wasserstein barycenters -- the…
We present a novel method for efficiently computing optimal transport maps and Wasserstein barycenters in high-dimensional spaces. Our approach uses conditional normalizing flows to approximate the input distributions as invertible…
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…
We consider robust variants of the standard optimal transport, named robust optimal transport, where marginal constraints are relaxed via Kullback-Leibler divergence. We show that Sinkhorn-based algorithms can approximate the optimal cost…
We study first order methods to compute the barycenter of a probability distribution $P$ over the space of probability measures with finite second moment. We develop a framework to derive global rates of convergence for both gradient…
We present a stochastic algorithm to compute the barycenter of a set of probability distributions under the Wasserstein metric from optimal transport. Unlike previous approaches, our method extends to continuous input distributions and…
In many applications in statistics and machine learning, the availability of data samples from multiple possibly heterogeneous sources has become increasingly prevalent. On the other hand, in distributionally robust optimization, we seek…