Optimal Poisson Subsampling for Softmax Regression

作     者：YAO Yaqiong ZOU Jiahui WANG Haiying YAO Yaqiong;ZOU Jiahui;WANG Haiying

作者机构：Department of StatisticsUniversity of ConnecticutStorrsCT06269USA School of StatisticsCapital University of Economics and BusinessBeijing 100070China 

出 版 物：《系统科学与复杂性学报:英文版》 (Journal of Systems Science and Complexity)

年 卷 期：2023年第36卷第4期

页      面：1609-1625页

核心收录：

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：Wang Haiying’s research was partially supported by the National Science Foundation under Grant No.CCF 2105571 

主　　题：Multinomial logistic regression optimality criterion optimal subsampling 

摘      要：Softmax regression,which is also called multinomial logistic regression,is widely used in various fields for modeling the relationship between covariates and categorical responses with multiple *** increasing volumes of data bring new challenges for parameter estimation in softmax regression,and the optimal subsampling method is an effective way to solve ***,optimal subsampling with replacement requires to access all the sampling probabilities simultaneously to draw a subsample,and the resultant subsample could contain duplicate *** this paper,the authors consider Poisson subsampling for its higher estimation accuracy and applicability in the scenario that the data exceed the memory *** authors derive the asymptotic properties of the general Poisson subsampling estimator and obtain optimal subsampling probabilities by minimizing the asymptotic variance-covariance matrix under both A-and L-optimality *** optimal subsampling probabilities contain unknown quantities from the full dataset,so the authors suggest an approximately optimal Poisson subsampling algorithm which contains two sampling steps,with the first step as a pilot *** authors demonstrate the performance of our optimal Poisson subsampling algorithm through numerical simulations and real data examples.