Title: Gaussian processes on the circle
Authors: Meng Li - Rice University (United States) [presenting]
Subhashis Ghosal - North Carolina State University (United States)
Abstract: Gaussian processes indexed by the circle provide a flexible model for closed curves, an one-dimensional object in two-dimensional space. Gaussian process often has the computational hurdle in its implementation that requires repeated matrix inversion, thus may not scale well. Focusing on the squared exponential Gaussian process on the circle, we obtain the analytical eigen-decomposition of its kernel, which enables efficient posterior sampling. We further conduct an extensive study of its reproducing kernel Hilbert space. An application to boundary detection problem in image process shows that squared exponential Gaussian process on the circle guarantees the geometric restriction of the boundary, leads to nearly minimax rate estimators adaptive to the smoothness of the boundary, and is computationally efficient.