Reproducing kernel Hilbert space based estimation of systems of ordinary differential equations

• Method to estimate the parameters of ODE models measured with noise.
• Reproducing kernel Hilbert space based regularization approach.
• Computationally efficient method with a wide range of applications.

Non-linear systems of differential equations have attracted the interest in fields like system biology, ecology or biochemistry, due to their flexibility and their ability to describe dynamical systems. Despite the importance of such models in many branches of science they have not been the focus of systematic statistical analysis until recently. 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 maximization of the penalized likelihood where the system of differential equations is used as a penalty. To do so, we use a reproducing kernel Hilbert space approach that allows us to formulate the estimation problem as an unconstrained numeric maximization problem easy to solve. The proposed method is tested with synthetically simulated data and it is used to estimate the unobserved transcription factor cdaR in Streptomyces coelicolor using gene expression data of the genes it regulates.