Stochastic Gradient Descent for Incomplete Tensor Linear Systems
For researchers working on tensor completion and large-scale linear systems, this provides a theoretical extension to handle more realistic missing data scenarios, though it is incremental.
This work extends stochastic gradient descent methods for solving incomplete tensor linear systems to non-uniform missing data patterns, proving convergence and validating on synthetic data.
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 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.