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Parameter Inference in Differential Equation Models of Biopathways Using Time Warped Gradient Matching

  • Mu Niu
  • Simon Rogers
  • Maurizio Filippone
  • Dirk Husmeier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10477)

Abstract

Parameter inference in mechanistic models of biopathways based on systems of coupled differential equations is a topical yet computationally challenging problem due to the fact that each parameter adaptation involves 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. Gradient matching critically hinges on the smoothing scheme for function interpolation, with spurious oscillations in the interpolant having a dramatic effect on the subsequent inference. The present article demonstrates that a time warping approach that aims to homogenize intrinsic functional length scales can lead to a significant improvement in parameter estimation accuracy. We demonstrate the effectiveness of this scheme on noisy data from a dynamical system with periodic limit cycle, and a biopathway model.

Keywords

Biopathways Differential equations Gradient matching Reproducing kernel hilbert space Time warping Optimisation 

Notes

Acknowledgments

This work was supported by EPSRC (EP/L020319/1). MF gratefully acknowledges support from the AXA Research Fund.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Mu Niu
    • 1
  • Simon Rogers
    • 3
  • Maurizio Filippone
    • 4
  • Dirk Husmeier
    • 2
  1. 1.School of Computing, Electronics and MathematicsPlymouth UniversityPlymouthUK
  2. 2.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK
  3. 3.Department of Computer ScienceUniversity of GlasgowGlasgowUK
  4. 4.Department of Data ScienceEurecomFrance

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