Wasserstein F-tests for Fr\'echet regression on Bures-Wasserstein manifolds

arXiv:2404.03878v1 Announce Type: cross
Abstract: This paper considers the problem of regression analysis with random covariance matrix as outcome and Euclidean covariates in the framework of Fr\'echet regression on the Bures-Wasserstein manifold. Such regression problems have many applications in single cell genomics and neuroscience, where we have covariance matrix measured over a large set of samples. Fr\'echet regression on the Bures-Wasserstein manifold is formulated as estimating the conditional Fr\'echet mean given covariates $x$. A non-asymptotic $\sqrt{n}$-rate of convergence (up to …

abstract analysis applications arxiv covariance framework genomics manifold matrix neuroscience paper random regression stat.me stat.ml tests type