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Adjoint-aided inference of Gaussian process driven differential equations
Paterne GAHUNGU · Christopher Lanyon · Mauricio A Álvarez · Engineer Bainomugisha · Michael T Smith · Richard Wilkinson

Wed Nov 30 09:00 AM -- 11:00 AM (PST) @ Hall J #909

Linear systems occur throughout engineering and the sciences, most notably as differential equations. In many cases the forcing function for the system is unknown, and interest lies in using noisy observations of the system to infer the forcing, as well as other unknown parameters. In differential equations, the forcing function is an unknown function of the independent variables (typically time and space), and can be modelled as a Gaussian process (GP). In this paper we show how the adjoint of a linear system can be used to efficiently infer forcing functions modelled as GPs, after using a truncated basis expansion of the GP kernel. We show how exact conjugate Bayesian inference for the truncated GP can be achieved, in many cases with substantially lower computation than would be required using MCMC methods. We demonstrate the approach on systems of both ordinary and partial differential equations, and show that the basis expansion approach approximates well the true forcing with a modest number of basis vectors. Finally, we show how to infer point estimates for the non-linear model parameters, such as the kernel length-scales, using Bayesian optimisation.

Author Information

Christopher Lanyon (University of Sheffield)
Mauricio A Álvarez (University of Manchester)
Engineer Bainomugisha (Makerere University)
Michael T Smith (University of Sheffield)

I’m currently a post-doc researcher at the University of Sheffield, in Neil Lawrence’s lab. We’re developing new tools to allow data to be anonymised, through the framework of differential privacy. As part of an innovate UK collaboration we’re building the scikic inference tool, which will provide both a conversation interface and a backend API for inferring demographic and lifestyle features about individuals. It is hoped it will be a useful tool to demonstrate the power of machine learning. In the future we hope to develop a user-centric data model for the analysis and storage of user data, with the motivation that personalised medicine and associated research requires access to user data. I spent most of 2014 lecturing at Makerere University, Kampala, Uganda. There I became involved in the field of Development Informatics, and have several on-going research topics; covering air pollution, nutrition-data, automated microscopy, traffic collision data and malaria distribution prediction. A variety of machine learning methods have been applied (for example Gaussian Process models for the model of malaria distribution). More details about some of these projects can be found at the Artificial Intelligence in the Developing World (AI-DEV) group’s website.

Richard Wilkinson (University of Nottingham)

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