Gaussian Processes
Gaussian Processes
Uwe D. Hanebeck
Several full-time, fully paid PhD/PostDoc positions in “Machine Learning for Estimation and Control under Uncertainty” at the Intelligent Sensor-Actuator-Systems Laboratory (ISAS), Karlsruhe Institute of Technology (KIT), Karlsruhe, Germany. We are seeking to fill several PhD/PostDoc positions in the following areas: Flow-based Bayesian state estimation, Deterministic sampling based on information measures, Intelligent distributed estimation architectures, Gaussian processes on manifolds for estimation of rigid body motion. All positions offer the possibility to cooperate with our network of partners from industry and academia on a national and international basis. We offer intensive mentoring and a quick path to the PhD degree (≤ 3 years). Besides research, the supervision of bachelor/master theses and participation in teaching is expected.
Deep kernel methods
Deep neural networks (DNNs) with the flexibility to learn good top-layer representations have eclipsed shallow kernel methods without that flexibility. Here, we take inspiration from deep neural networks to develop a new family of deep kernel method. In a deep kernel method, there is a kernel at every layer, and the kernels are jointly optimized to improve performance (with strong regularisation). We establish the representational power of deep kernel methods, by showing that they perform exact inference in an infinitely wide Bayesian neural network or deep Gaussian process. Next, we conjecture that the deep kernel machine objective is unimodal, and give a proof of unimodality for linear kernels. Finally, we exploit the simplicity of the deep kernel machine loss to develop a new family of optimizers, based on a matrix equation from control theory, that converges in around 10 steps.
Multi-resolution Multi-task Gaussian Processes: London air pollution
Poor air quality in cities is a significant threat to health and life expectancy, with over 80% of people living in urban areas exposed to air quality levels that exceed World Health Organisation limits. In this session, I present a multi-resolution multi-task framework that handles evidence integration under varying spatio-temporal sampling resolution and noise levels. We have developed both shallow Gaussian Process (GP) mixture models and deep GP constructions that naturally handle this evidence integration, as well as biases in the mean. These models underpin our work at the Alan Turing Institute towards providing spatio-temporal forecasts of air pollution across London. We demonstrate the effectiveness of our framework on both synthetic examples and applications on London air quality. For further information go to: https://www.turing.ac.uk/research/research-projects/london-air-quality. Collaborators: Oliver Hamelijnck, Theodoros Damoulas, Kangrui Wang and Mark Girolami.
Hida-Matern Gaussian Processes
COSYNE 2022
Hida-Matern Gaussian Processes
COSYNE 2022