Stochastic Gradient Descent for Linear Systems with Missing Data  

作　　者：Anna Ma Deanna Needell 

机构地区：[1]Claremont Graduate University,Claremont,CA 91711,USA [2]University of California,Los Angeles,Los Angeles CA 90095,USA

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2019年第1期1-20,共20页高等学校计算数学学报（英文版）

基　　金：Needell was partially supported by NSF CAREER Grant No.1348721,NSF BIGDATA 1740325;the Alfred P.Sloan Fellowship.Ma was supported in part by NSF CAREER Grant No.1348721,the CSRC Intellisis Fellowship;the Edison Interna-tional Scholarship.

摘　　要：Traditional methods for solving linear systems have quickly become imprac-tical due to an increase in the size of available data.Utilizing massive amounts of data is further complicated when the data is incomplete or has missing entries.In this work,we address the obstacles presented when working with large data and incom-plete data simultaneously.In particular,we propose to adapt the Stochastic Gradient Descent method to address missing data in linear systems.Our proposed algorithm,the Stochastic Gradient Descent for Missing Data method(mSGD),is introduced and theoretical convergence guarantees are provided.In addition,we include numerical experiments on simulated and real world data that demonstrate the usefulness of our method.

关 键 词：Linear systems missing data iterative methods least squares problems 

分 类 号：O17[理学—数学]