相关论文: Averaging on the Bures-Wasserstein manifold: dimen…

We explore a robust version of the barycenter problem among $n$ centered Gaussian probability measures, termed Semi-Unbalanced Optimal Transport (SUOT)-based Barycenter, wherein the barycenter remains fixed while the others are relaxed…

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…

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…

The Wasserstein barycenter is a geometric construct which captures the notion of centrality among probability distributions, and which has found many applications in machine learning. However, most algorithms for finding even an approximate…

In this paper, we present an adaptive gradient descent method for geodesically convex optimization on a Riemannian manifold with nonnegative sectional curvature. The method automatically adapts to the local geometry of the function and does…

Euclidean gradient descent algorithms barely capture the geometry of objective function-induced hypersurfaces and risk driving update trajectories off the hypersurfaces. Riemannian gradient descent algorithms address these issues but fail…

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…

This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…

We further research on the accelerated optimization phenomenon on Riemannian manifolds by introducing accelerated global first-order methods for the optimization of $L$-smooth and geodesically convex (g-convex) or $\mu$-strongly g-convex…

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 consider the problem of computing a Wasserstein barycenter for a set of discrete probability distributions with finite supports, which finds many applications in areas such as statistics, machine learning and image processing. When the…

We prove the large deviations principle for empirical Bures-Wasserstein barycenters of independent, identically-distributed samples of covariance matrices and covariance operators. As an application, we explore some consequences of our…

Various statistical tasks, including sampling or computing Wasserstein barycenters, can be reformulated as fixed-point problems for operators on probability distributions. Accelerating standard fixed-point iteration schemes provides a…

We study the problem of finding the global Riemannian center of mass of a set of data points on a Riemannian manifold. Specifically, we investigate the convergence of constant step-size gradient descent algorithms for solving this problem.…

We develop a new Riemannian descent algorithm that relies on momentum to improve over existing first-order methods for geodesically convex optimization. In contrast, accelerated convergence rates proved in prior work have only been shown to…

The Wasserstein barycenter extends the Euclidean mean to the space of probability measures by minimizing the weighted sum of squared 2-Wasserstein distances. We develop a free-support algorithm for computing Wasserstein barycenters that…

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…

From optimal transport to robust dimensionality reduction, a plethora of machine learning applications can be cast into the min-max optimization problems over Riemannian manifolds. Though many min-max algorithms have been analyzed in the…

Gradient descent methods are fundamental first-order optimization algorithms in both Euclidean spaces and Riemannian manifolds. However, the exact gradient is not readily available in many scenarios. This paper proposes a novel inexact…

We study the convergence of the Riemannian steepest descent algorithm on the Grassmann manifold for minimizing the block version of the Rayleigh quotient of a symmetric matrix. Even though this problem is non-convex in the Euclidean sense…