Robust parameter estimation for dynamical systems from outlier-corrupted data
Corinna Maier (1,2), Carolin Loos (1,2), Jan Hasenauer (1,2)
(1) Helmholtz Zentrum München, Germany, (2) Technische Universität München, Germany
Objectives: Dynamics of cellular processes are often studied using mechanistic mathematical models. These models possess unknown parameters which are generally estimated from experimental data assuming normally distributed measurement noise [1]. Outlier corruption of datasets often cannot be avoided. These outliers may distort parameter estimates, resulting in incorrect model predictions. Robust parameter estimation methods are required which provide reliable parameter estimates in the presence of outliers.
Methods: We propose and evaluate methods for estimating the parameters of ordinary differential equation models from outlier-corrupted data. As alternatives to the normal distribution as noise distribution, we consider the Laplace, the Huber, the Cauchy and the Student's t distribution. Therefore, we derive the necessary gradients and Hessian matrices of the objective function to ensure an efficient optimization.
Results: We assess accuracy, robustness and computational efficiency of estimators using these different distribution assumptions. To this end, we consider artificial data of a conversion process, as well as published experimental data for Epo-induced JAK/STAT signaling [2]. We study how well the methods can compensate and discover artificially introduced outliers.
Conclusions: Our evaluation reveals that using alternative distributions improves the robustness of parameter estimates [3].
References:
[1] Raue,A. et al. (2009) Structural and practical identifiability analysis of partially observed dynamical models by exploiting the profile likelihood. Bioinformatics, 28, i529-i534
[2] Swameye,I. et al. (2003) Identification of nucleocytoplasmic cycling as a remote sensor in cellular signaling by databased modeling. Proc. Natl. Acad. Sci. U.S.A., 100, 1028-1033
[3] Maier,C. et al. (2017) Robust parameter estimation for dynamical systems from outlier-corrupted data. Bioinformatics btw703. doi: 10.1093/bioinformatics/btw703
