Statistics seminar

Abstract: Given a planar curve, imagine rolling a sphere along that curve without slipping or twisting, and by this means tracing out a curve on the sphere. Such a rolling operation induces a local isometry between the sphere and the plane so that the two curves uniquely determine each other, and moreover, the operation extends to a general class of manifold M in any dimension d.

I will describe how rolling can be used to construct an analogue of a Gaussian process with values in M, known as a rolled Gaussian process, starting from an R^d -valued Gaussian process with mean m and covariance K. I will discuss the relationship between m and the Frechet mean of the rolled process, and using the inverse operations of unrolling and unwrapping, discuss simple estimators of m and K and their convergence rates. Utility of the model will be shown in an application involving curves on 3D orientations coming from a robot learning experiment.