Path-wise, spectral, and geometric perspectives on Gaussian processes

· Talk · University of Oxford

Abstract. Gaussian processes are usually studied via their finite-dimensional marginal distributions, but this is not the only way to think about them. In this talk, I discuss a little-known result relating Gaussian process priors to posteriors in a path-wise rather than distributional manner, and show how it can be leveraged for efficient posterior sampling. I conclude with a discussion on different ways of specifying Gaussian process priors, focusing on non-Euclidean settings via techniques based on stochastic partial differential equations, of particular interest for applications in the physical sciences and robotics.