Stochastic Gradient Descent for Linear Systems with Missing Data
For practitioners dealing with large-scale linear systems that have missing entries, this offers a scalable solution with theoretical backing.
The paper adapts Stochastic Gradient Descent to solve large linear systems with missing data, providing theoretical convergence guarantees and demonstrating effectiveness on simulated and real-world data.
Traditional methods for solving linear systems have quickly become impractical 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 incomplete 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.