SQUIDS Seminar - A State-Space Perspective on Modelling and Inference for Online Skill Rating
| Dates: | 13 December 2023 |
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| Times: | 15:00 - 16:00 |
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| What is it: | Seminar |
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| Organiser: | Department of Mathematics |
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| Who is it for: | University staff, External researchers, Current University students |
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| Speaker: | Simon Urbainczyk |
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Schedule:
- 3:05pm: research talk 'Computational Methods for Bayesian Imaging with Deep Gaussian Process Priors'
Abstract: In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that incorporates prior information which is then updated through Bayes' formula. Finding a prior is difficult. Images often exhibit non-stationary effects and multiscale behaviour. Thus, usual Gaussian process priors are not suitable. Deep Gaussian processes, on the other hand, encode non-stationary behaviour in a natural way through their hierarchical structure.
To apply Bayes' formula, one commonly employs a Markov chain Monte Carlo method that requires sampling from the prior. In the case of deep Gaussian processes, sampling is especially challenging in high dimensions: the associated covariance matrices are large, dense, and changing from sample to sample. A popular strategy towards decreasing computational complexity is to view Gaussian processes as the solutions to a fractional stochastic partial differential equation (SPDE). In this work, we investigate efficient computational strategies to solve the fractional SPDEs occurring in deep Gaussian process sampling. Indeed, we employ rational approximations to represent the fractional operators through sparse matrices and reduce computational cost from cubic to near-linear. We test our techniques in standard Bayesian image reconstruction problems.
Speaker
Simon Urbainczyk
Organisation: Heriot-Watt
Travel and Contact Information
Find event
G.114
Alan Turing Building
Manchester
