R package for statistical inference in dynamical systems using kernel based gradient matching: KGode

Niu, M., Wandy, J., Daly, R. , Rogers, S. and Husmeier, D. (2021) R package for statistical inference in dynamical systems using kernel based gradient matching: KGode. Computational Statistics, 36(1), pp. 715-747. (doi: 10.1007/s00180-020-01014-x)

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Abstract

Many processes in science and engineering can be described by dynamical systems based on nonlinear ordinary differential equations (ODEs). Often ODE parameters are unknown and not directly measurable. Since nonlinear ODEs typically have no closed form solution, standard iterative inference procedures require a computationally expensive numerical integration of the ODEs every time the parameters are adapted, which in practice restricts statistical inference to rather small systems. To overcome this computational bottleneck, approximate methods based on gradient matching have recently gained much attention. The idea is to circumvent the numerical integration step by using a surrogate cost function that quantifies the discrepancy between the derivatives obtained from a smooth interpolant to the data and the derivatives predicted by the ODEs. The present article describes the software implementation of a recent method that is based on the framework of reproducing kernel Hilbert spaces. We provide an overview of the methods available, illustrate them on a series of widely used benchmark problems, and discuss the accuracy–efficiency trade-off of various regularization methods.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Daly, Dr Ronan and Wandy, Dr Joe and Husmeier, Professor Dirk and Niu, Dr Mu and Rogers, Dr Simon
Authors: Niu, M., Wandy, J., Daly, R., Rogers, S., and Husmeier, D.
College/School:College of Medical Veterinary and Life Sciences > Institute of Cancer Sciences
College of Science and Engineering > School of Computing Science
College of Science and Engineering > School of Mathematics and Statistics
Journal Name:Computational Statistics
Publisher:Springer
ISSN:0943-4062
ISSN (Online):1613-9658
Published Online:23 July 2020
Copyright Holders:Copyright © 2020 The Authors
First Published:First published in Computational Statistics 36(1): 715-747
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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Project CodeAward NoProject NamePrincipal InvestigatorFunder's NameFunder RefLead Dept
190760Computational inference in systems biologyDirk HusmeierEngineering and Physical Sciences Research Council (EPSRC)EP/L020319/1M&S - Statistics
173707Institutional Strategic Support Fund (2016)Anna DominiczakWellcome Trust (WELLCOTR)204820/Z/16/ZInstitute of Cardiovascular & Medical Sciences