Variational Bayesian inference for CP tensor completion with side information

@article{Budzinskiy2022VariationalBI,
  title={Variational Bayesian inference for CP tensor completion with side information},
  author={S Budzinskiy and Nikolai Zamarashkin},
  journal={ArXiv},
  year={2022},
  volume={abs/2206.12486}
}
We propose a message passing algorithm, based on variational Bayesian inference, for low-rank tensor completion with automatic rank determination in the canonical polyadic format when additional side information (SI) is given. The SI comes in the form of low-dimensional subspaces the contain the fiber spans of the tensor (columns, rows, tubes, etc.). We validate the regularization properties induced by SI with extensive numerical experiments on synthetic and real-world data and present the… 

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