Semi-parametric Statistical Inference And Application Of Gene Regulatory Network

The gene regulatory networks are of great significance for biological research and play an important role in disease treatment and so on.With the development of high-throughput detection technology,a large number of dynamic high-dimensional gene expression data has emerged,providing opportunities and challenges for the accurate reconstruction of gene regulatory networks.Differential equation is an important method for studying the reconstruction of gene regulatory networks.At present,a great quantity of scholars have made assumptions of the parametric and non-parametric models for the function form of the rightside in the differential equation.This article considers the assumption of a partial linear single index model on the right-side function,and the advantage of this semi-parametric model is that it not only considers the linear regulation between genes,but also considers the nonlinear comprehensive regulation.In this paper,we first use the independence test to conduct a preliminary screening for high-dimensional variables,construct a partial linear single index ordinary differential equation model,use the profile least squares method for parameter estimation,and then use the smoothly clipped absolute deviation(SCAD)method to select variables and prove the consistency of variable selection.Second,because the regulatory relationship between genes is directional,in order to test the significance of the parameters in the model,this paper proposes a partial linear single index ordinary differential equation model based on the likelihood ratio test of the directed graph,proves the asymptotic property of likelihood ratio tests statistics,and extends the likelihood ratio tests of directed acyclic graph.Numerical simulation demonstrates the superior properties in small samples with the proposed model and method;in the empirical analysis,we use the recall rate as an evaluation criterion and reconstruct 10 gene regulation subnets with yeast and E.coli gene expression data sets.All show higher recall rate,indicating that the method proposed in this paper is more adaptable to the data set.