Iterative State Estimation in Non-linear Dynamical Systems Using Approximate Expectation Propagation

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.

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.

Probabilistic software analysis methods extend classic static analysis techniques to consider the effects of probabilistic uncertainty, whether explicitly embedded within the code – as in probabilistic programs – or externalized in a probabilistic input distribution.

Modeling distributions on Riemannian manifolds is a crucial component in understanding non-Euclidean data that arises, e.g., in physics and geology. We propose a class of flows that uses convex potentials from Riemannian optimal transport.

In this work, we quantify the discretisation error induced by gradient descent in two-player games, and use that to understand and improve such games, including Generative Adversarial Networks. Two-player games Many machine learning applications involve not one single model, but two models which get trained jointly.

Gaussian processes are a model class for learning unknown functions from data. They are particularly of interest in statistical decision-making systems, due to their ability to quantify and propagate uncertainty. In this work, we study analogs of the popular Matérn class where the domain of the Gaussian process is replaced by a weighted undirected graph.

Meta-learning can make machine learning algorithms more data-efficient, using experience from prior tasks to learn related tasks quicker. Since some tasks will be more-or-less informative with respect to performance on any given task in a domain, an interesting question to consider is, how might a meta-learning algorithm automatically choose an informative task to learn? Here we summarise probabilistic active meta-learning (PAML): a meta-learning algorithm that uses latent task representations to rank and select informative tasks to learn next.

Learning models of physical systems can sometimes be difficult. Vanilla neural networks—like residual networks—particularly struggle to learn invariant properties like the conservation of energy which is fundamental to physical systems.

Learning models of physical systems can be tricky, but exploiting inductive biases about the nature of the system can speed up learning significantly. In the following, we will give a brief overview and the key insights behind variational integrator networks.