Advertisement

Riemannian Distances between Covariance Operators and Gaussian Processes

  • Minh Hà QuangEmail author
Conference paper
  • 111 Downloads
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

In thisworkwe study several recently formulated Riemannian distances between infinite-dimensional positive definite Hilbert-Schmidt operators in the context of covariance operators associated with functional random processes. Specifically, we focus on the affine-invariant Riemannian and Log-Hilbert-Schmidt distances and the family of Alpha Procrustes distances, which include both the Bures-Wasserstein and Log-Hilbert-Schmidt distances as special cases. In particular, we present finitedimensional approximations of the infinite-dimensional distances and show their convergence to the exact distances. The theoretical formulation is illustrated with numerical experiments on covariance operators of Gaussian processes.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Copyright information

© Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.RIKEN Center for Advanced Intelligence ProjectTokyoJapan

Personalised recommendations