Variables Screening Of Ultra-high Dimensional Single-index Model With Missing Data

Variable screening has been widely used in various life scenarios.For example,when investigating the key genes for diseases,the number of genes that may affect diseases is much larger than the number of patient sample we can obtained.Missing data often occurs during the acquisition and preservation of genetic data.However,it is important to screen effective variables in such ultra-high dimensional data with missing data,which can locate key genes of the disease.Furthermore,it has significance for later precision medicine and disease prevention.Considering the complexity of gene data and “dimension disaster” of ultra-high dimensional data,we will use single-index models to explore this problem.Therefore,in the case of random missing response variables,this paper mainly studies the variable screening problem of ultra-high dimensional single-index models.Based on inverse probability weighting and deterministic independent variable screening methods,this paper proposes a method based on MSIS(Sure Independence Screening Method with Missing data)and we construct the variable screening utensil on this method to solve this problem.Firstly,we use the K-S statistics and Logistic regression model to estimate the inverse probability weights;Secondly,we can establish an inverse probability weighted quadratic loss function for each covariate variable and the utility function values of all covariate variables can be arranged in ascending in order to reduce the dimension of the data set to a suitable size;Finally,the inverse probability weighted least squares method based on LASSO penalty is used to select more refined variables for the reduced-dimensional data to complete the selection of important variables.Furthermore,a large number of numerical simulations are used to show that the variable screening utensil constructed based on MSIS has good performance and stable effect.What’s more,MSIS is also stable to the missing rate.In addition,the effect of peripheral blood gene profile data on the MSIS method was used to judge performance,and it was found that MSIS can play an important role in the exploration of key genes with missing data and can also be extended to other fields.