On marginal sliced inverse regression for ultrahigh dimensional model-free feature selection
This paper aims to develop selection consistency for ultrahigh dimensional settings. An approach called marginal sliced inverse regression (SIR) is proposed for model-free feature screening and variable selection. Two distinct procedures, Dantzig selector and sparse precision matrix estimation, are incorporated to get two versions of sample level marginal SIR utilities. Both procedures lead to model-free variable selection consistency with predictor dimensionality \(p\) diverging at an exponential rate of the sample size \(n\). As a special case of marginal SIR, the correlation among the predictors is ignored and marginal independence SIR is proposed. Marginal independence SIR is closely related to many existing independence screening procedures in the literature, and achieves model-free screening consistency in the ultrahigh dimensional setting. The finite sample performances of the proposed procedures are studied through synthetic examples and an application to the small round blue cell tumour data is given.
scientific article; zbMATH DE number 6684021