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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Publisher's URL: http://proceedings.mlr.press/v37/macdonald15.html
Abstract
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 |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| 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 |
| Publisher: | PMLR |
| ISSN: | 1938-7228 |
| 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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