Abstract
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.
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References
Andrews, D.W.K.: The block-block boostrap: improved asymptotic refinements. Econometrica 72(3), 673–700 (2004)
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)
Braithwaite, A.W., Royds, J.A., Jackson, P.: The p53 story: layers of complexity. Carcinogenesis 26(7), 1161–1169 (2005)
Breiman, L.: Random forests. Machine Learning 45(1), 5–32 (2001)
Brewer, D.: Modelling the p53 gene regulatory network. Ph.D. thesis, University of London (2006)
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)
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)
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)
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)
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)
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)
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)
Cussens, J.: Parameter estimation in stochastic logic programs. Machine Learning 44(3), 245–271 (2001)
Davidson, E., Levin, M.: Gene regulatory networks. Proc. Natl. Acad. Sci. USA 102(14), 4935 (2005)
Efron, B.: The Jackknife, the Bootstrap and other Resampling Plans. Society for Industrial and Applied Mathematics, Philadelphia (1982)
Efron, B.: Bootstrap methods: another look at the jackknife. The Annals of Statistics 7(1), 1–26 (1997)
Efron, B., Tibshirani, R.: An introduction to bootstrap. Chapman and Hall, Boca Raton (1993)
Elliot, W., Elliot, D.: Biochemistry and Molecular Biology, 2nd edn. Oxford University Press, Oxford (2002)
Fridman, J.S., Lowe, S.W.: Control of apoptosis by p53. Oncogene 22(56), 9030–9040 (2003)
Gelman, A., Carlin, J.B., Stern, H.S., Rubin, D.B.: Bayesian Data Analysis. Chapman and Hall/CRC (2004)
Girolami, M.: Bayesian inference for differential equations. Theoretical Computer Science 408(1), 4–16 (2008)
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)
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)
Levins, R.: The strategy of model building in population biology. American Scientist 54(421-429) (1966)
Lodhi, H.: Advances in systems biology. In: Lodhi, H., Muggleton, S. (eds.) Elements of Computational Systems Biology. Wiley, Hoboken (2010)
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)
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)
Rao, J.S., Tibshirani, R.: The out-of-bootstrap method for model averaging and selection. Tech. rep., University of Toronto (1997)
Tyson, J.: Models of cell cycle control in eukaryotes. Journal of Biotechnology 71(1-3), 239–244 (1999)
Vogelstein, B., Lane, D., Levine, A.: Surfing the p53 network. Nature 408(6810), 307–310 (2000)
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)
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)
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)
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Lodhi, H., Gilbert, D. (2011). Bootstrapping Parameter Estimation in Dynamic Systems. In: Elomaa, T., Hollmén, J., Mannila, H. (eds) Discovery Science. DS 2011. Lecture Notes in Computer Science(), vol 6926. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24477-3_17
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DOI: https://doi.org/10.1007/978-3-642-24477-3_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-24476-6
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