Title: Regularization of parameter estimation in ordinary differential equations via discrete optimal control theory
Authors: Quentin Clairon - Newcastle University (United Kingdom) [presenting]
Abstract: A parameter estimation method in Ordinary Differential Equation (ODE) models from partial, noisy observations is presented. Due to complex relationships between parameters and states, standard techniques such as nonlinear least squares can lead to presence of poorly identifiable parameters. Moreover, ODEs are generally approximations of the true process and influence of this misspecification on inference is often neglected. Control theories have been used to regularize the problem of parameter estimation in this context. In these methods, a perturbation is added to the ODE to facilitate data fitting and to represent model misspecifications. The estimation is done by solving a trade-off between data and model fidelity which leads to solve an optimal control problem. However, these approaches based on continuous control theory are computationally intensive and rely on a nonparametric state estimator known to be biased in sparse sample case. We construct a criterion based on discrete control theory. A computational efficient method which also bypasses the presmoothing step of signal estimation is developed. First, we expose how the estimation problem is turned into a control one and the numerical method used to solve it. Then, we derive the consistency with root-n convergence rate of our estimator in the well-specified case. Simulation in models with poorly identifiable parameters and misspecifications presence show our method gives accurate estimates.