Statistical inference in mechanistic models: time warping for improved gradient matching

Niu, M., Macdonald, B. , Rogers, S. , Filippone, M. and Husmeier, D. (2018) Statistical inference in mechanistic models: time warping for improved gradient matching. Computational Statistics, 33(2), pp. 1091-1123. (doi: 10.1007/s00180-017-0753-z)

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Inference in mechanistic models of non-linear differential equations is a challenging problem in current computational statistics. Due to the high computational costs of numerically solving the differential equations in every step of an iterative parameter adaptation scheme, approximate methods based on gradient matching have become popular. However, these methods critically depend on the smoothing scheme for function interpolation. The present article adapts an idea from manifold learning and demonstrates that a time warping approach aiming to homogenize intrinsic length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from two dynamical systems with periodic limit cycle, a biopathway, and an application from soft-tissue mechanics. Our study also provides a comparative evaluation on a wide range of signal-to-noise ratios.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Filippone, Dr Maurizio and Niu, Dr Mu and Husmeier, Professor Dirk and Macdonald, Dr Benn and Rogers, Dr Simon
Authors: Niu, M., Macdonald, B., Rogers, S., Filippone, M., and Husmeier, D.
College/School:College of Science and Engineering > School of Computing Science
College of Science and Engineering > School of Mathematics and Statistics > Statistics
Journal Name:Computational Statistics
ISSN (Online):1613-9658
Published Online:09 August 2017
Copyright Holders:Copyright © 2017 The Authors
First Published:First published in Computational Statistics 33(2): 1091-1123
Publisher Policy:Reproduced under a Creative Commons License

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