Variational Bayesian inference for CP tensor completion with side information

TL;DR

This paper introduces a variational Bayesian message passing algorithm for low-rank tensor completion that leverages side information to improve recovery accuracy and reduce sample complexity.

Contribution

It presents a novel Bayesian inference method for tensor completion that automatically determines tensor rank using side information in the CP format.

Findings

SI reduces the number of samples needed for successful tensor recovery

The method effectively determines tensor rank automatically

Numerical experiments validate the regularization effect of side information

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.