Abstract
Gaussian process (GP) regression is a powerful tool in
non-parametric regression providing uncertainty estimates.
However, it is limited to data in vector spaces. In fields
such as shape analysis and diffusion tensor imaging, the
data often lies on a manifold, making GP regression nonviable, as the resulting predictive distribution does not live
in the correct geometric space. We tackle the problem by
defining wrapped Gaussian processes (WGPs) on Riemannian manifolds, using the probabilistic setting to generalize GP regression to the context of manifold-valued targets.
The method is validated empirically on diffusion weighted
imaging (DWI) data, directional data on the sphere and in
the Kendall shape space, endorsing WGP regression as an
efficient and flexible tool for manifold-valued regression