Estimating time-varying gene regulation network
The problem of modeling the dynamic feature within a gene regulation network is of great interest for a long time. We propose to model this dynamical system with a set of ordinary differential equations (ODEs), in which the regulation function is estimated directly from data without any parametric assumption. Most current research assumes the gene regulation network is static, but in reality the connection and regulation function of the network may change with time or environment. This change is reflected in our dynamical model by modelling the regulation function varying with gene expression and allowing this regulation function to be zero if no regulation happens. We introduce a statistical method called `functional fSCAD' to estimate a time-varying sparse gene regulation network, and, simultaneously, to provide a smooth estimator for the regulation function and identify the interval in which no regulation exists. The performance of the proposed method for finite sample is investigated in a carefully-designed Monte Carlo simulation study. Our method is also demonstrated by estimating a sparse network related to 79 genes involved in the life cycle of Drosophila melanogaster.