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.
翻译:我们建议一种信息传递算法,以不同贝叶斯推论为基础,用于在提供补充侧面信息(SI)时,以卡尼科多立体格式自动定级完成低声震动,以自动定级。SI以低维次空间的形式出现,内含高压线(柱、行、管等)的纤维跨度。我们用大量关于合成和现实世界数据的数字实验来验证SI引证的正规化特性,并介绍关于振动恢复和定级的结果。结果显示,在SI在场的情况下,成功完成所需的样本数量会大大减少。我们还讨论了在SI的维度与强力相似时存在的阶段过渡曲线的缘由。