Volume 12, Issue 1
Stochastic Gradient Descent for Linear Systems with Missing Data

Anna Ma & Deanna Needell

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 1-20.

Published online: 2018-09

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  • Abstract

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.

  • Keywords

Linear systems, missing data, iterative methods, least squares problems.

  • AMS Subject Headings

65F10, 65F20, 68W20

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{NMTMA-12-1, author = {}, title = {Stochastic Gradient Descent for Linear Systems with Missing Data}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2018}, volume = {12}, number = {1}, pages = {1--20}, abstract = {

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.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0066}, url = {http://global-sci.org/intro/article_detail/nmtma/12689.html} }
TY - JOUR T1 - Stochastic Gradient Descent for Linear Systems with Missing Data JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 1 EP - 20 PY - 2018 DA - 2018/09 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0066 UR - https://global-sci.org/intro/article_detail/nmtma/12689.html KW - Linear systems, missing data, iterative methods, least squares problems. AB -

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.

Anna Ma & Deanna Needell. (2020). Stochastic Gradient Descent for Linear Systems with Missing Data. Numerical Mathematics: Theory, Methods and Applications. 12 (1). 1-20. doi:10.4208/nmtma.OA-2018-0066
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