Variational Bayesian inference for CP tensor completion with side information
CoRR(2022)
Abstract
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 results about tensor recovery and
rank determination. The results show that the number of samples required for
successful completion is significantly reduced in the presence of SI. We also
discuss the origin of a bump in the phase transition curves that exists when
the dimensionality of SI is comparable with that of the tensor.
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Key words
cp tensor completion,variational bayesian inference
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