19 February 2021

Mu Niu (University of Glasgow) INTRINSIC GAUSSIAN PROCESSES ON NONLINEAR MANIFOLDS AND POINT CLOUDS

We propose a class of intrinsic Gaussian processes (GPs) for interpolation, regression on manifolds with a primary focus on complex constrained domains or irregularly shaped spaces arising as subsets or submanifolds of R, R2, R3 and beyond. For example, intrinsic GPs can accommodate spatial domains arising as complex subsets of Euclidean space. Intrinsic GPs respect the potentially complex boundary or interior conditions as well as the intrinsic geometry of the spaces. The key novelty of the approach proposed is to utilize the relationship between heat kernels and the transition density of Brownian motion on manifolds for constructing and approximating valid and computationally feasible covariance kernels.