Variational Bayesian inference for CP tensor completion with side information
This work addresses tensor completion with side information, which is an incremental improvement for applications in data analysis and machine learning where additional structural knowledge is available.
The authors tackled the problem of low-rank tensor completion with automatic rank determination in the canonical polyadic format by proposing a variational Bayesian inference message passing algorithm that incorporates side information in the form of low-dimensional subspaces. The results show that the number of samples required for successful completion is significantly reduced in the presence of side information, with a noted bump in phase transition curves when the dimensionality of side information is comparable to that of the tensor.
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.