Bootstrapping Parameter Estimation in Dynamic Systems

  • Huma Lodhi
  • David Gilbert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6926)


We propose a novel approach for parameter estimation in dynamic systems. The method is based on the use of bootstrapping for time series data. It estimates parameters within the least square framework. The data points that do not appear in the individual bootstrapped datasets are used to assess the goodness of fit and for adaptive selection of the optimal parameters.

We evaluate the efficacy of the proposed method by applying it to estimate parameters of dynamic biochemical systems. Experimental results show that the approach performs accurate estimation in both noise-free and noisy environments, thus validating its effectiveness. It generally outperforms related approaches in the scenarios where data is characterized by noise.


Extracellular Signal Regulate Kinase Ataxia Telangiectasia Mutate Noisy Environment Little Square Estimator Mouse Double Minute 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Andrews, D.W.K.: The block-block boostrap: improved asymptotic refinements. Econometrica 72(3), 673–700 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Bar-Or, R.L., Maya, R., Segel, L.A., Alon, U., Levine, A.J., Oren, M.: Generation of oscillations by the p53-mdm2 feedback loop: a theoretical and experimental study. Proc. Natl. Acad. Sci. USA 97(21), 11250–11255 (2000)CrossRefGoogle Scholar
  3. 3.
    Braithwaite, A.W., Royds, J.A., Jackson, P.: The p53 story: layers of complexity. Carcinogenesis 26(7), 1161–1169 (2005)CrossRefGoogle Scholar
  4. 4.
    Breiman, L.: Random forests. Machine Learning 45(1), 5–32 (2001)CrossRefzbMATHGoogle Scholar
  5. 5.
    Brewer, D.: Modelling the p53 gene regulatory network. Ph.D. thesis, University of London (2006)Google Scholar
  6. 6.
    Brewer, D., Barenco, M., Callard, R., Hubank, M., Stark, J.: Fitting ordinary differential equations to short time course data. Philosophical Transactions of the Royal Society A 366, 519–544 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Calder, M., Gilmore, S., Hillston, J.: Modelling the influence of RKIP on the ERK signalling pathway using the stochastic process algebra PEPA. In: Priami, C., Ingólfsdóttir, A., Mishra, B., Riis Nielson, H. (eds.) Transactions on Computational Systems Biology VII. LNCS (LNBI), vol. 4230, pp. 1–23. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. 8.
    Calderhead, B., Girolami, M., Lawrence, N.: Accelerating bayesian inference over nonlinear differentail equations with gaussian processes. Advances in Neural Information Processing System 21, 217–224 (2009)Google Scholar
  9. 9.
    Cho, K.H., Shin, S.Y., Kim, H.W., Wolkenhauer, O., Mcferran, B., Kolch, W.: Mathematical modeling of the influence of RKIP on the ERK signaling pathway. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 127–141. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  10. 10.
    Ciliberto, A., Novak, B., Tyson, J.J.: Steady states and oscillations in the p53/mdm2 network cell cycle. Cell Cycle 4(3), 488–493 (2005)CrossRefGoogle Scholar
  11. 11.
    Coleman, T.F., Li, Y.: On the convergence of reflective Newton methods for large-scale nonlinear minimization subject to bounds. Mathematical Programming 67(2), 189–224 (1994)MathSciNetCrossRefzbMATHGoogle Scholar
  12. 12.
    Coleman, T.F., Li, Y.: An interior, trust region approach for nonlinear minimization subject to bounds. SIAM Journal on Optimization 6(2), 418–445 (1996)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Cussens, J.: Parameter estimation in stochastic logic programs. Machine Learning 44(3), 245–271 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Davidson, E., Levin, M.: Gene regulatory networks. Proc. Natl. Acad. Sci. USA 102(14), 4935 (2005)CrossRefGoogle Scholar
  15. 15.
    Efron, B.: The Jackknife, the Bootstrap and other Resampling Plans. Society for Industrial and Applied Mathematics, Philadelphia (1982)CrossRefzbMATHGoogle Scholar
  16. 16.
    Efron, B.: Bootstrap methods: another look at the jackknife. The Annals of Statistics 7(1), 1–26 (1997)MathSciNetCrossRefzbMATHGoogle Scholar
  17. 17.
    Efron, B., Tibshirani, R.: An introduction to bootstrap. Chapman and Hall, Boca Raton (1993)CrossRefzbMATHGoogle Scholar
  18. 18.
    Elliot, W., Elliot, D.: Biochemistry and Molecular Biology, 2nd edn. Oxford University Press, Oxford (2002)zbMATHGoogle Scholar
  19. 19.
    Fridman, J.S., Lowe, S.W.: Control of apoptosis by p53. Oncogene 22(56), 9030–9040 (2003)CrossRefGoogle Scholar
  20. 20.
    Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC (2004)Google Scholar
  21. 21.
    Girolami, M.: Bayesian inference for differential equations. Theoretical Computer Science 408(1), 4–16 (2008)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Gunawardena, J.: Models in systems biology: the parameter problem and the meanings of robustness. In: Lodhi, H., Muggleton, S. (eds.) Elements of Computational Systems Biology, vol. 1. Wiley, Hoboken (2010)Google Scholar
  23. 23.
    Kirk, P.D.W., Stumpf, P.H.: Gaussian process regression bootstrapping: exploring the effects of uncertainty in time course data. Bioinformatics 25(10), 1300–1306 (2009)CrossRefGoogle Scholar
  24. 24.
    Levins, R.: The strategy of model building in population biology. American Scientist 54(421-429) (1966)Google Scholar
  25. 25.
    Lodhi, H.: Advances in systems biology. In: Lodhi, H., Muggleton, S. (eds.) Elements of Computational Systems Biology. Wiley, Hoboken (2010)CrossRefGoogle Scholar
  26. 26.
    Lodhi, H., Muggleton, S.: Modelling metabolic pathways using stochastic logic programs-based ensemble methods. In: Danos, V., Schachter, V. (eds.) CMSB 2004. LNCS (LNBI), vol. 3082, pp. 119–133. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  27. 27.
    Ramsay, J.O., Hooker, G., Campbell, D., Cao, J.: Parameter estimation for differential equations: a generalized smoothing approach. J. R. Statist. Soc. B 69(5), 741–796 (2007)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Rao, J.S., Tibshirani, R.: The out-of-bootstrap method for model averaging and selection. Tech. rep., University of Toronto (1997)Google Scholar
  29. 29.
    Tyson, J.: Models of cell cycle control in eukaryotes. Journal of Biotechnology 71(1-3), 239–244 (1999)CrossRefGoogle Scholar
  30. 30.
    Vogelstein, B., Lane, D., Levine, A.: Surfing the p53 network. Nature 408(6810), 307–310 (2000)CrossRefGoogle Scholar
  31. 31.
    Yeung, K., Seitz, T., Li, S., Janosch, P., McFerran, B., Kaiser, C., Fee, F., Katsanakis, K.D., Rose, D.W., Mischak, H., Sedivy, J.M., Kolch, W.: Suppression of Raf-1 kinase activity and MAP kinase signaling by RKIP. Nature 401, 173–177 (1999)CrossRefGoogle Scholar
  32. 32.
    Yeung, K., Janosch, P., McFerran, B., Rose, D.W., Mischak, H., Sedivy, J.M., Kolch, W.: Mechanism of suppression of the Raf/MEK/Extracellular signal-regulated kinase pathway by the Raf kinase inhibitor protein. Mol. Cell Biol. 20(9), 3079–3085 (2000)CrossRefGoogle Scholar
  33. 33.
    Yonish-Rouach, Y., Resnitzky, D., Lotem, J., Sachs, L., Kimchi, A., Oren, M.: Wild-type p53 induces apoptosis of myeloid leukaemic cells that is inhibited by interleukin-6. Nature 352(6333), 345–347 (1991)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Huma Lodhi
    • 1
  • David Gilbert
    • 1
  1. 1.School of Information Systems, Computing and MathematicsBrunel UniversityUK

Personalised recommendations