Research On Variable Screening Of Ultra-high Dimensional Categorical Data Based On Relative Entrop

With the cost reduction of data collection and more and more data characteris-tics,a large number of ultra-high-dimensional data are produced.The primary task of analyzing ultra-high dimensional data is dimensionality reduction.The traditional dimensionality reduction method is usually variable selection,but it is limited by com-putational cost,statistical accuracy and algorithm stability.In ultra-high dimensional data,it is also common for explanatory variables and response variables to be classi-fied data.Therefore,based on relative entropy,this paper proposes a variable screening method for ultra-high-dimensional data when the response variables are two classification and multi classification.Firstly,when the response variable is binary data,a new variable screening method for ultra-high dimensional binary data is proposed.Using the characteristics of rela-tive entropy,this method calculates the relative entropy of the marginal distribution of covariate(3₅)under the two values of response variable(4,and constructs a variable screening method（KL-SIS）for ultra-high-dimensional two classification data based on relative entropy.Under certain regularity conditions,it is proved that KL-SIS method meets the property of variable screening.Then,through numerical simulation and exam-ple analysis,this paper compares the proposed method with the four variable screening methods of CIES,IG-SIS,PC-SIS and KF.Simulation and case analysis results show that the accuracy of the proposed method is higher than other screening methods.Secondly,when the response variable is multi classification data,a variable screening method for ultra-high-dimensional multi classification data is proposed.Specifically,it is to calculate the relative entropy of the marginal distribution of covariate(3₅)under each category of response variable(4 and the marginal distribution of covariate(3₅)under unconditional constraints,and then take the proportion of each category as the weight to obtain the weighted average,and construct a multi classification variable screening method based on weighted relative entropy（WKL-SIS）.The variable screening property of this method is also proved under the condition of regularity.In this paper,taking the three classification data as an example,it is proved that WKL-SIS method also has a good effect of screening variables through numerical simulation and example analysis.