Generalized Tikhonov regularization in estimation of systems of differential equations with applications

Ernst Wit (University of Groningen)

Thursday 3rd November, 2016 14:15-15:00 Maths 204

Abstract

Non-linear systems of ordinary differential equations (ODE) are a staple modelling tool in System Biology, Ecology or Biochemistry. The reasons of the generalized use of these models are their flexibility and ability to describe dynamical systems. Despite the importance of ODE models, they have not been the focus of systematic statistical analysis until the last few years. In this work we propose a general approach to estimate the parameters of systems of differential equations measured with noise. Our methodology is based on the generalized Tychonov regularization where the differential system of equations is used as a penalty. Using this strategy, the solution of the ODE is not required which allows us to deal with large systems in which some components might be unobserved. We show the utility of the proposed method in a variety of scenarios ranging from the identification of gene regulatory networks to the estimation of the parameters of metabolic networks.

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