A1197
Title: A Riemannian covariance for manifold-valued data
Authors: Meshal Abuqrais - King\'s College London (United Kingdom) [presenting]
Davide Pigoli - King's College London (United Kingdom)
Abstract: The extension of bivariate measures of dependence to non-Euclidean spaces is a challenging problem. The non-linear nature of these spaces makes the generalization of classical measures of linear dependence (such as the covariance) not trivial. The aim is to propose a novel approach to measure stochastic dependence between two random variables taking values in a Riemannian manifold, with the aim of both generalizing the classical concepts of covariance and correlation and building a connection to Frechet moments of random variables on manifolds. The purpose is to introduce generalized local measures of covariance and correlation, and it is shown that the latter is a natural extension of Pearson correlation. Then, suitable estimators are proposed for these quantities, and strong consistency results are proven. Finally, their effectiveness is demonstrated through simulated examples and a real-world application.
