Barycenters and a Law of Large Numbers in Gromov Hyperbolic Spaces
Offered By: Applied Algebraic Topology Network via YouTube
Course Description
Overview
Explore barycenters of probability measures on Gromov hyperbolic spaces in this 51-minute lecture. Delve into the development of convex optimization in metric spaces, examining the contraction property in terms of the Wasserstein distance and a form of law of large numbers for stochastic approximation of barycenters. Discover how these findings generalize corresponding results on CAT(0)-spaces, with additional terms dependent on the hyperbolicity constant.
Syllabus
Shin-ichi Ohta (6/23/23): Barycenters and a law of large numbers in Gromov hyperbolic spaces
Taught by
Applied Algebraic Topology Network
Related Courses
Regularization for Optimal Transport and Dynamic Time Warping Distances - Marco CuturiAlan Turing Institute via YouTube Analysis of Mean-Field Games - Lecture 1
International Centre for Theoretical Sciences via YouTube Why Should Q=P in the Wasserstein Distance Between Persistence Diagrams?
Applied Algebraic Topology Network via YouTube Washington Mio - Stable Homology of Metric Measure Spaces
Applied Algebraic Topology Network via YouTube Wasserstein Distributionally Robust Optimization - Theory and Applications in Machine Learning
Institute for Pure & Applied Mathematics (IPAM) via YouTube