Partial Suffcient Dimension Reduction of Categorical Predictors Based on LASSO

The sliced inverse regression (SIR) method has achieved significant success in the fields of dimension reduction and data visualization by fully reducing dimensions. With the development of information collection technology, high-dimensional data have emerged in large quantities, and classical dimension reduction methods based on all features for analysis will encounter overfitting problems. In this paper, we introduce the categorical predictors based on SIR and apply LASSO for feature selection to propose the LASSO-PSIR method. We also prove the consistency of this estimation method. Numerical simulations show that the LASSO-PSIR method can fully consider the influence of categorical predictors while retaining the original information, and better recover the partial central subspace.