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 ...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.展开更多
基金Needell was partially supported by NSF CAREER Grant No.1348721,NSF BIGDATA 1740325the Alfred P.Sloan Fellowship.Ma was supported in part by NSF CAREER Grant No.1348721,the CSRC Intellisis Fellowshipthe Edison Interna-tional Scholarship.
文摘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.
