Related papers: Statistical inference for Bures-Wasserstein baryce…
Quasi-set theory provides us a mathematical background for dealing with collections of indistinguishable elementary particles. In this paper, we show how to obtain the usual statistics (Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac)…
Dataset Distillation (DD) aims to generate a compact synthetic dataset that enables models to achieve performance comparable to training on the full large dataset, significantly reducing computational costs. Drawing from optimal transport…
Recent investigations of turbulent circulation fluctuations have uncovered substantial insights into the statistical organization of flow structures and revealed unexpected geometric features of turbulent intermittency. Of particular…
This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…
We study the problem of estimating the barycenter of a distribution given i.i.d. data in a geodesic space. Assuming an upper curvature bound in Alexandrov's sense and a support condition ensuring the strong geodesic convexity of the…
In a variety of research areas, the weighted bag of vectors and the histogram are widely used descriptors for complex objects. Both can be expressed as discrete distributions. D2-clustering pursues the minimum total within-cluster variation…
Wasserstein distances are metrics on probability distributions inspired by the problem of optimal mass transportation. Roughly speaking, they measure the minimal effort required to reconfigure the probability mass of one distribution in…
We study barycenters in the space of probability measures on a Riemannian manifold, equipped with the Wasserstein metric. Under reasonable assumptions, we establish absolute continuity of the barycenter of general measures $\Omega \in…
Wasserstein barycenter is the centroid of a collection of discrete probability distributions which minimizes the average of the $\ell_2$-Wasserstein distance. This paper focuses on the computation of Wasserstein barycenters under the case…
The Frechet mean or barycenter generalizes the idea of averaging in spaces where pairwise addition is not well-defined. In general metric spaces, the Frechet sample mean is not a consistent estimator of the theoretical Frechet mean. For…
We introduce and study a variant of the Wasserstein distance on the space of probability measures, specially designed to deal with measures whose support has a dendritic, or treelike structure with a particular direction of orientation. Our…
Inspired by recent advances in distributed algorithms for approximating Wasserstein barycenters, we propose a novel distributed algorithm for this problem. The main novelty is that we consider time-varying computational networks, which are…
Wasserstein barycenters provide a principled approach for aggregating probability measures, while preserving the geometry of their ambient space. Existing discrete methods are not scalable as they assume access to the complete set of…
Optimal transport maps between two probability distributions $\mu$ and $\nu$ on $\mathbb{R}^d$ have found extensive applications in both machine learning and statistics. In practice, these maps need to be estimated from data sampled…
This work presents an algorithm to sample from the Wasserstein barycenter of absolutely continuous measures. Our method is based on the gradient flow of the multimarginal formulation of the Wasserstein barycenter, with an additive…
We consider the rate-limited quantum-to-classical optimal transport in terms of output-constrained rate-distortion coding for both finite-dimensional and continuous-variable quantum-to-classical systems with limited classical common…
Computing the Wasserstein barycenter of a set of probability measures under the optimal transport metric can quickly become prohibitive for traditional second-order algorithms, such as interior-point methods, as the support size of the…
We develop a general theory to address a consensus-based combination of estimations in a parallelized or distributed estimation setting. Taking into account the possibility of very discrepant estimations, instead of a full consensus we…
Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties. In short, the barycenter task is to take the average of a collection of probability…
We study the extrinsic Bures--Wasserstein geometry of the determinant-normalized Kronecker model $\mcK_n=\{V\ot U:U,V\in\Sp^n,\ \det U=1\}\subset\Sp^{n^2}$, asking when the ambient Bures geodesic between two Kronecker positive definite…