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，也称为多维数组，是机器学习和统计学中有用的数据结构。近年来，贝叶斯方法已成为分析张量值数据的流行方向，因为它们为模型引入稀疏性并进行不确定性量化提供了便捷途径。本文概述了用于解决张量补全和回归问题的频率学派方法和贝叶斯方法，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、先验分配、后验计算及理论性质。此外，我们还讨论了该领域的潜在未来方向。