Stochastic algorithms for computing means of probability measures

DOI10.1016/j.spa.2011.12.011zbMath1262.60073arXiv1106.5106OpenAlexW2025983125MaRDI QIDQ424479

Marc Arnaudon, Le Yang, Anthony Phan, Clément Dombry

Publication date: 1 June 2012

Published in: Stochastic Processes and their Applications (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.5106

zbMATH Keywords

Riemannian geometryconvexityMarkov chaingeodesic ballmeaninvariance principleprobability measurebarycenter

Mathematics Subject Classification ID

Computational methods in Markov chains (60J22) Discrete-time Markov processes on general state spaces (60J05) Strong limit theorems (60F15) Integration on manifolds; measures on manifolds (58C35)

Related Items (13)

Estimating the geometric median in Hilbert spaces with stochastic gradient algorithms: \(L^p\) and almost sure rates of convergence ⋮ A hyperbolic approach for learning communities on graphs ⋮ A stochastic algorithm finding generalized means on compact manifolds ⋮ A diffusion process associated with Fréchet means ⋮ Rank-preserving geometric means of positive semi-definite matrices ⋮ Characterization of barycenters in the Wasserstein space by averaging optimal transport maps ⋮ Convergence Analysis of Gradient Algorithms on Riemannian Manifolds without Curvature Constraints and Application to Riemannian Mass ⋮ Efficient and fast estimation of the geometric median in Hilbert spaces with an averaged stochastic gradient algorithm ⋮ A Robbins–Monro-type algorithm for computing global minimizer of generalized conic functions ⋮ Riemannian \(L^p\) averaging on Lie group of nonzero quaternions ⋮ Discrete-time gradient flows and law of large numbers in Alexandrov spaces ⋮ Riemannian barycentres of Gibbs distributions: new results on concentration and convexity in compact symmetric spaces ⋮ On the measure of the cut locus of a Fréchet mean

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• Convexity and the Hemisphere
• Estimation of Riemannian Barycentres
• On Stochastic Processes Defined by Differential Equations with a Small Parameter

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