Statistical Methods for High-Dimensional ODEs with Application to Dynamic Network Modeling

The gene regulation network (GRN) is a high-dimensional complex system, which can be represented by various mathematical or statistical models. The ordinary differential equation (ODE) model is one of the popular dynamic GRN models. In this talk, I introduce a few high-dimensional ODE models, coupled with ODE estimation methods and SCAD techniques, to model dynamic GRNs that could flexibly deal with linear and nonlinear regulation effects. The asymptotic properties of the proposed method are established in ``large p, small n" setting. Simulation studies are performed to validate the proposed approach. An application example for identifying the dynamic GRN of T-cell activation is used to illustrate the usefulness of the proposed method.