| With the rapid development of data acquisition technology,a lot of high-dimensional data has emerged in fields such as medicine,biology,signal processing,and highfrequency transactions.Since there are a large number of independent variables that are not related to the dependent variable in high-dimensional data sets,it is very difficult to perform statistical analysis on high-dimensional data sets,so it is particularly important to select variables before statistical analysis.This paper proposes a model-free variable selection(VSM-SDR)algorithm based on stepwise dimensionality reduction.The VSM-SDR algorithm introduces a subset splicing method including two variable selection strategies,which improves the speed of variable selection.The VSM-SDR algorithm is a model-free variable selection method,so it effectively avoids the reduction in the accuracy of subsequent statistical analysis caused by incorrect model selection.In addition,the VSM-SDR algorithm only uses the kernel function of the sufficient dimensionality reduction method,so variable selection can also be based on other sufficient dimensionality reduction methods.This paper theoretically proves the selection consistency of the VSM-SDR algorithm based on slice inverse regression method and slice mean variance estimation method.After a large number of experiments,it is confirmed that the VSM-SDR algorithm can not only determine the number of selected variables adaptively,but also has great advantages for variable selection of high-dimensional sparse data.We also extends the algorithm framework to non-Euclidean spaces and have achieved well performance. |
