ODE parameter inference using adaptive gradient matching with Gaussian processes

Frank Dondelinger, Dirk Husmeier, Simon Rogers, Maurizio Filippone
Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, PMLR 31:216-228, 2013.

Abstract

Parameter inference in mechanistic models based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the need to follow each parameter adaptation with a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differential equations, offer a computationally appealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently sampling from the joint distribution of the ODE parameters and GP hyperparameters. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a detailed comparison with the method in Calderhead et al. (2008) and the explicit ODE integration approach, both in terms of parameter inference accuracy and in terms of computational efficiency.

Cite this Paper


BibTeX
@InProceedings{pmlr-v31-dondelinger13a, title = {ODE parameter inference using adaptive gradient matching with Gaussian processes}, author = {Dondelinger, Frank and Husmeier, Dirk and Rogers, Simon and Filippone, Maurizio}, booktitle = {Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics}, pages = {216--228}, year = {2013}, editor = {Carvalho, Carlos M. and Ravikumar, Pradeep}, volume = {31}, series = {Proceedings of Machine Learning Research}, address = {Scottsdale, Arizona, USA}, month = {29 Apr--01 May}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v31/dondelinger13a.pdf}, url = {http://proceedings.mlr.press/v31/dondelinger13a.html}, abstract = {Parameter inference in mechanistic models based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the need to follow each parameter adaptation with a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differential equations, offer a computationally appealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently sampling from the joint distribution of the ODE parameters and GP hyperparameters. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a detailed comparison with the method in Calderhead et al. (2008) and the explicit ODE integration approach, both in terms of parameter inference accuracy and in terms of computational efficiency.} }
Endnote
%0 Conference Paper %T ODE parameter inference using adaptive gradient matching with Gaussian processes %A Frank Dondelinger %A Dirk Husmeier %A Simon Rogers %A Maurizio Filippone %B Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2013 %E Carlos M. Carvalho %E Pradeep Ravikumar %F pmlr-v31-dondelinger13a %I PMLR %P 216--228 %U http://proceedings.mlr.press/v31/dondelinger13a.html %V 31 %X Parameter inference in mechanistic models based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the need to follow each parameter adaptation with a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differential equations, offer a computationally appealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently sampling from the joint distribution of the ODE parameters and GP hyperparameters. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a detailed comparison with the method in Calderhead et al. (2008) and the explicit ODE integration approach, both in terms of parameter inference accuracy and in terms of computational efficiency.
RIS
TY - CPAPER TI - ODE parameter inference using adaptive gradient matching with Gaussian processes AU - Frank Dondelinger AU - Dirk Husmeier AU - Simon Rogers AU - Maurizio Filippone BT - Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics DA - 2013/04/29 ED - Carlos M. Carvalho ED - Pradeep Ravikumar ID - pmlr-v31-dondelinger13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 31 SP - 216 EP - 228 L1 - http://proceedings.mlr.press/v31/dondelinger13a.pdf UR - http://proceedings.mlr.press/v31/dondelinger13a.html AB - Parameter inference in mechanistic models based on systems of coupled differential equations is a topical yet computationally challenging problem, due to the need to follow each parameter adaptation with a numerical integration of the differential equations. Techniques based on gradient matching, which aim to minimize the discrepancy between the slope of a data interpolant and the derivatives predicted from the differential equations, offer a computationally appealing shortcut to the inference problem. The present paper discusses a method based on nonparametric Bayesian statistics with Gaussian processes due to Calderhead et al. (2008), and shows how inference in this model can be substantially improved by consistently sampling from the joint distribution of the ODE parameters and GP hyperparameters. We demonstrate the efficiency of our adaptive gradient matching technique on three benchmark systems, and perform a detailed comparison with the method in Calderhead et al. (2008) and the explicit ODE integration approach, both in terms of parameter inference accuracy and in terms of computational efficiency. ER -
APA
Dondelinger, F., Husmeier, D., Rogers, S. & Filippone, M.. (2013). ODE parameter inference using adaptive gradient matching with Gaussian processes. Proceedings of the Sixteenth International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 31:216-228 Available from http://proceedings.mlr.press/v31/dondelinger13a.html.

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