Controversy in mechanistic modelling with Gaussian processes

Benn Macdonald, Catherine Higham, Dirk Husmeier
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1539-1547, 2015.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-macdonald15, title = {Controversy in mechanistic modelling with Gaussian processes}, author = {Macdonald, Benn and Higham, Catherine and Husmeier, Dirk}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1539--1547}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/macdonald15.pdf}, url = {https://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.} }
Endnote
%0 Conference Paper %T Controversy in mechanistic modelling with Gaussian processes %A Benn Macdonald %A Catherine Higham %A Dirk Husmeier %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-macdonald15 %I PMLR %P 1539--1547 %U https://proceedings.mlr.press/v37/macdonald15.html %V 37 %X 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.
RIS
TY - CPAPER TI - Controversy in mechanistic modelling with Gaussian processes AU - Benn Macdonald AU - Catherine Higham AU - Dirk Husmeier BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-macdonald15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1539 EP - 1547 L1 - http://proceedings.mlr.press/v37/macdonald15.pdf UR - https://proceedings.mlr.press/v37/macdonald15.html AB - 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. ER -
APA
Macdonald, B., Higham, C. & Husmeier, D.. (2015). Controversy in mechanistic modelling with Gaussian processes. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1539-1547 Available from https://proceedings.mlr.press/v37/macdonald15.html.

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