Tensors, also known as multidimensional arrays, are useful data structures in machine learning and statistics. In recent years, Bayesian methods have emerged as a popular direction for analyzing tensor-valued data since they provide a convenient way to introduce sparsity into the model and conduct uncertainty quantification. In this article, we provide an overview of frequentist and Bayesian methods for solving tensor completion and regression problems, with a focus on Bayesian methods. We review common Bayesian tensor approaches including model formulation, prior assignment, posterior computation, and theoretical properties. We also discuss potential future directions in this field.

翻译：张量（又称多维数组）是机器学习和统计学中的实用数据结构。近年来，贝叶斯方法已成为分析张量值数据的主流方向，因为它们为模型引入稀疏性及进行不确定性量化提供了便捷途径。本文概述了解决张量补全与回归问题的频率学派及贝叶斯方法，重点关注贝叶斯方法。我们回顾了常见的贝叶斯张量方法，包括模型构建、先验设定、后验计算及理论性质。此外，还探讨了该领域潜在的未来研究方向。