Controversy in mechanistic modelling with Gaussian processes

Macdonald, B., Higham, C. and Husmeier, D. (2015) Controversy in mechanistic modelling with Gaussian processes. Proceedings of Machine Learning Research, 37, pp. 1539-1547.

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Parameter inference in mechanistic models based on non-affine differential equations is computationally onerous, and various faster alternatives based on gradient matching have been proposed. A particularly promising approach is based on nonparametric Bayesian modelling with Gaussian processes, which exploits the fact that a Gaussian process is closed under differentiation. However, two alternative paradigms have been proposed. The first paradigm, proposed at NIPS 2008 and AISTATS 2013, is based on a product of experts approach and a marginalization over the derivatives of the state variables. The second paradigm, proposed at ICML 2014, is based on a probabilistic generative model and a marginalization over the state variables. The claim has been made that this leads to better inference results. In the present article, we offer a new interpretation of the second paradigm, which highlights the underlying assumptions, approximations and limitations. In particular, we show that the second paradigm suffers from an intrinsic identifiability problem, which the first paradigm is not affected by.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Higham, Dr Catherine and Husmeier, Professor Dirk and Macdonald, Dr Benn
Authors: Macdonald, B., Higham, C., and Husmeier, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Statistics
University Services > Learning and Teaching Services Division
Journal Name:Proceedings of Machine Learning Research
Journal Abbr.:JMLR WCP
ISSN (Online):1533-7928
Copyright Holders:Copyright © 2015 The Authors
First Published:First published in Proceedings of Machine Learning Research 37: 1539-1547
Publisher Policy:Reproduced with the permission of the authors
Data DOI:10.5525/gla.researchdata.283

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
633291Computational inference in systems biologyDirk HusmeierEngineering & Physical Sciences Research Council (EPSRC)EP/L020319/1M&S - STATISTICS