It is common for datasets to contain both categorical and continuous variables. However, many feature screening methods designed for high-dimensional classification assume that the variables are continuous. This limit...It is common for datasets to contain both categorical and continuous variables. However, many feature screening methods designed for high-dimensional classification assume that the variables are continuous. This limits the applicability of existing methods in handling this complex scenario. To address this issue, we propose a model-free feature screening approach for ultra-high-dimensional multi-classification that can handle both categorical and continuous variables. Our proposed feature screening method utilizes the Maximal Information Coefficient to assess the predictive power of the variables. By satisfying certain regularity conditions, we have proven that our screening procedure possesses the sure screening property and ranking consistency properties. To validate the effectiveness of our approach, we conduct simulation studies and provide real data analysis examples to demonstrate its performance in finite samples. In summary, our proposed method offers a solution for effectively screening features in ultra-high-dimensional datasets with a mixture of categorical and continuous covariates.展开更多
In ultra-high-dimensional data, it is common for the response variable to be multi-classified. Therefore, this paper proposes a model-free screening method for variables whose response variable is multi-classified fro...In ultra-high-dimensional data, it is common for the response variable to be multi-classified. Therefore, this paper proposes a model-free screening method for variables whose response variable is multi-classified from the point of view of introducing Jensen-Shannon divergence to measure the importance of covariates. The idea of the method is to calculate the Jensen-Shannon divergence between the conditional probability distribution of the covariates on a given response variable and the unconditional probability distribution of the covariates, and then use the probabilities of the response variables as weights to calculate the weighted Jensen-Shannon divergence, where a larger weighted Jensen-Shannon divergence means that the covariates are more important. Additionally, we also investigated an adapted version of the method, which is to measure the relationship between the covariates and the response variable using the weighted Jensen-Shannon divergence adjusted by the logarithmic factor of the number of categories when the number of categories in each covariate varies. Then, through both theoretical and simulation experiments, it was demonstrated that the proposed methods have sure screening and ranking consistency properties. Finally, the results from simulation and real-dataset experiments show that in feature screening, the proposed methods investigated are robust in performance and faster in computational speed compared with an existing method.展开更多
文摘It is common for datasets to contain both categorical and continuous variables. However, many feature screening methods designed for high-dimensional classification assume that the variables are continuous. This limits the applicability of existing methods in handling this complex scenario. To address this issue, we propose a model-free feature screening approach for ultra-high-dimensional multi-classification that can handle both categorical and continuous variables. Our proposed feature screening method utilizes the Maximal Information Coefficient to assess the predictive power of the variables. By satisfying certain regularity conditions, we have proven that our screening procedure possesses the sure screening property and ranking consistency properties. To validate the effectiveness of our approach, we conduct simulation studies and provide real data analysis examples to demonstrate its performance in finite samples. In summary, our proposed method offers a solution for effectively screening features in ultra-high-dimensional datasets with a mixture of categorical and continuous covariates.
文摘In ultra-high-dimensional data, it is common for the response variable to be multi-classified. Therefore, this paper proposes a model-free screening method for variables whose response variable is multi-classified from the point of view of introducing Jensen-Shannon divergence to measure the importance of covariates. The idea of the method is to calculate the Jensen-Shannon divergence between the conditional probability distribution of the covariates on a given response variable and the unconditional probability distribution of the covariates, and then use the probabilities of the response variables as weights to calculate the weighted Jensen-Shannon divergence, where a larger weighted Jensen-Shannon divergence means that the covariates are more important. Additionally, we also investigated an adapted version of the method, which is to measure the relationship between the covariates and the response variable using the weighted Jensen-Shannon divergence adjusted by the logarithmic factor of the number of categories when the number of categories in each covariate varies. Then, through both theoretical and simulation experiments, it was demonstrated that the proposed methods have sure screening and ranking consistency properties. Finally, the results from simulation and real-dataset experiments show that in feature screening, the proposed methods investigated are robust in performance and faster in computational speed compared with an existing method.
