Statistical inference for missing data is common in data analysis, and there are still widespread cases of missing data in big data. The literature has discussed the practicability of two-stage feature screening with categorical covariates missing at random (IMCSIS). Therefore, we propose group feature screening for ultrahigh-dimensional data with categorical covariates missing at random (GIMCSIS), which can be used to effectively select important features. The proposed method expands the scope of IMCSIS and further improves the performance of classification learning when covariates are missing. Based on the adjusted Pearson chi-square statistics, a two-stage group feature screening method is modeled, and theoretical analysis proves that the proposed method conforms to the sure screening property. In a numerical simulation, GIMCSIS can achieve better finite sample performance under binary and multivariate response variables and multi-classification covariates. The empirical analysis through multiple classification results shows that GIMCSIS is superior to IMCSIS in imbalanced data classification.

Currently, most of the ultra-high-dimensional feature screening methods for categorical data are based on the correlation between covariates and response variables, using some statistics as the screening index to screen important covariates. Thus, with the increasing number of data types and model availability limitations, there may be a potential problem with the existence of a class of unimportant covariates that are also highly correlated with the response variable due to their high correlation with the other covariates. To address this issue, in this paper, we establish a model-free feature screening procedure for binary categorical response variables from the perspective of the contribution of features to classification. The idea is to introduce the Jensen-Shannon divergence to measure the difference between the conditional probability distributions of the covariates when the response variables take on different values. The larger the value of the Jensen-Shannon divergence, the stronger the covariate's contribution to the classification of the response variable, and the more important the covariate is. We propose two kinds of model-free ultra-high-dimensional feature screening methods for binary response data. Meanwhile, the methods are suitable for continuous or categorical covariates. When the numbers of covariate categories are the same, the feature screening is based on traditional Jensen-Shannon divergence. When the numbers of covariate categories are different, the Jensen-Shannon divergence is adjusted using the logarithmic factor of the number of categories. We theoretically prove that the proposed methods have sure screening and ranking consistency properties, and through simulations and real data analysis, we demonstrate that, in feature screening, the approaches proposed in this paper have the advantages of effectiveness, stability, and less computing time compared with an existing method.

Because the majority of model-free feature screening methods concentrate on individual predictors, they are unable to consider structured predictors, such as grouped variables. In this study, we suggest a model-free and direct extension of the original sure independence screening approach for group screening using Gini impurity for a classification model. Compared to current feature screening approaches, the proposed method performs better in terms of screening efficiency and classification accuracy. It was established that the suggested group screening process exhibits sure screening properties and ranking consistency properties under specific regularity conditions. We used simulation studies to illustrate the limited sample performance of the proposed technique and real data analysis.

To identify critical genomes that influence a cancer patient's survival time, feature screening methods play a vital role in this biomedical field. Most of the current research relies on a fixed survival function model, which limits its universality in practical applications. In this paper, we propose the Generalized Jaccard coefficient (GJAC), which extends the traditional Jaccard coefficient from comparing binary vectors' similarity to calculating the correlation between the general vectors. The larger the GJAC value, the higher the sample similarity. Using the GJAC, we introduce a novel model-free screening method to select the active set of covariates in ultra-high dimensional survival data. Through Monte Carlo simulations, GJAC-Sure Independence Screening (GJAC-SIS) shows a higher accuracy, lower errors, and an excellent applicability in different types of survival data compared with other existing model-free feature screening methods in survival data. Additionally, in the real cancer datasets (DLBCL), GJAC-SIS can screen out two additional important genomes, which are certified in the real biomedical experiment, while the other five methods can't. As a result, GJAC-SIS achieves a high screening precision, delivers a more effective screening outcome, and has a better utility and universality.