We are a research group at UCL’s Centre for Artificial Intelligence. Our research expertise is in data-efficient machine learning, probabilistic modeling, and autonomous decision making. Applications focus on robotics, climate science, nuclear fusion, and sustainable development.

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SML Group in November 2022

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.

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

Bayesian inference in non-linear dynamical systems seeks to find good posterior approximations of a latent state given a sequence of observations. Gaussian filters and smoothers, including the (extended/unscented) Kalman filter/smoother, which are commonly used in engineering applications, yield Gaussian posteriors on the latent state. While they are computationally efficient, they are often criticised for their crude approximation of the posterior state distribution. In this paper, we address this criticism by proposing a message passing scheme for iterative state estimation in non-linear dynamical systems, which yields more informative (Gaussian) posteriors on the latent states. Our message passing scheme is based on expectation propagation (EP). We prove that classical Rauch–Tung–Striebel (RTS) smoothers, such as the extended Kalman smoother (EKS) or the unscented Kalman smoother (UKS), are special cases of our message passing scheme. Running the message passing scheme more than once can lead to significant improvements of the classical RTS smoothers, so that more informative state estimates can be obtained. We address potential convergence issues of EP by generalising our state estimation framework to damped updates and the consideration of general alpha-divergences.

As Gaussian processes are used to answer increasingly complex questions, analytic solutions become scarcer and scarcer. Monte Carlo methods act as a convenient bridge for connecting intractable mathematical expressions with actionable estimates via sampling. Conventional approaches for simulating Gaussian process posteriors view samples as draws from marginal distributions of process values at finite sets of input locations. This distribution-centric characterization leads to generative strategies that scale cubically in the size of the desired random vector. These methods are prohibitively expensive in cases where we would, ideally, like to draw high-dimensional vectors or even continuous sample paths. In this work, we investigate a different line of reasoning: rather than focusing on distributions, we articulate Gaussian conditionals at the level of random variables. We show how this pathwise interpretation of conditioning gives rise to a general family of approximations that lend themselves to efficiently sampling Gaussian process posteriors. Starting from first principles, we derive these methods and analyze the approximation errors they introduce. We, then, ground these results by exploring the practical implications of pathwise conditioning in various applied settings, such as global optimization and reinforcement learning.