Research Blog

State estimation in nonlinear systems is difficult due to the non-Gaussianity of posterior state distributions. For linear systems, an exact solution is attained by running the Kalman filter/smoother. However for nonlinear systems, one typically relies on either crude Gaussian approximations by linearising the system (e.

I am writing this post a day after running our latest UCL-MOAP workshop on “Bayesian Machine Learning for Weather and Climate” to reflect on the event while my memory is fresh.

Gaussian processes are machine learning models capable of learning unknown functions with uncertainty. Motivated by a desire to deploy Gaussian processes in novel areas of science, we present a new class of Gaussian processes that model random vector fields on Riemannian manifolds that is (1) mathematically sound, (2) constructive enough for use by machine learning practitioners and (3) trainable using standard methods such as inducing points.