The sole aim of this book is to give a self-contained introduction to concepts and mathematical tools in Bayesian matrix decomposition in order to seamlessly introduce matrix decomposition techniques and their applications in subsequent sections. However, we clearly realize our inability to cover all the useful and interesting results concerning Bayesian matrix decomposition and given the paucity of scope to present this discussion, e.g., the separated analysis of variational inference for conducting the optimization. We refer the reader to literature in the field of Bayesian analysis for a more detailed introduction to the related fields. This book is primarily a summary of purpose, significance of important Bayesian matrix decomposition methods, e.g., real-valued decomposition, nonnegative matrix factorization, Bayesian interpolative decomposition, and the origin and complexity of the methods which shed light on their applications. The mathematical prerequisite is a first course in statistics and linear algebra. Other than this modest background, the development is self-contained, with rigorous proof provided throughout.

翻译：本书的唯一目标是提供关于贝叶斯矩阵分解的概念和数学工具的自包含介绍，以便无缝地在后续章节中引入矩阵分解技术及其应用。然而，我们清楚地认识到，我们无法涵盖所有关于贝叶斯矩阵分解的有用且有趣的结果，并且由于讨论范围的局限性，例如，无法单独分析用于优化的变分推理。我们建议读者参考贝叶斯分析领域的文献，以获取对相关领域的更详细介绍。本书主要是对重要贝叶斯矩阵分解方法（例如实值分解、非负矩阵分解、贝叶斯插值分解）的目的、意义以及这些方法起源和复杂性的总结，这些内容揭示了其应用前景。数学预备知识需要一门统计学和线性代数的基础课程。除此之外，本书内容自包含，并提供贯穿全文的严格证明。