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<p>Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed in&#xa0;[1] that this problem can be tackled using a stochastic gradient descent-based method, assuming that the missing data follows a uniform missing pattern. We adapt the technique by modifying the update direction, showing that the method is applicable under other missing data models. We prove convergence results and experimentally verify these results on synthetic data.</p>

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Stochastic Gradient Descent for Incomplete Tensor Linear Systems

  • 期刊论文

  • 发表日期：

    2026年6月23日

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  • Anna Ma,
  • Deanna Needell,
  • Alexander Xue

摘要

Solving large tensor linear systems poses significant challenges due to the high volume of data stored, and it only becomes more challenging when some of the data is missing. Recently, Ma et al. showed in [1] that this problem can be tackled using a stochastic gradient descent-based method, assuming that the missing data follows a uniform missing pattern. We adapt the technique by modifying the update direction, showing that the method is applicable under other missing data models. We prove convergence results and experimentally verify these results on synthetic data.