论文标题
CP张量完成的变异贝叶斯推断，并提供侧面信息
Variational Bayesian inference for CP tensor completion with side information
论文作者
论文摘要
我们提出了一个基于变异贝叶斯推断的消息传递算法，以进行低级张量的完成，并在给出其他侧面信息（SI）时，在规范多地格式中进行自动排名确定。 Si以低维子空间的形式出现，其中包含张量的纤维跨度（列，行，管等）。我们通过对合成和现实世界数据进行广泛的数值实验来验证SI诱导的正则化属性，并介绍有关张量恢复和等级确定的结果。结果表明，在SI存在下，成功完成所需的样品数量大大减少。我们还讨论了当Si的尺寸与张量相媲美时存在的相变曲线中凸起的起源。
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.
