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.

介绍 Bayesian matrix decomposition 及其方法的目的、意义、起源和复杂性，包括 real-valued decomposition、nonnegative matrix factorization 和 Bayesian interpolative decomposition，数学预备知识为统计学和线性代数的初级课程，提供了严格的证明。

贝叶斯矩阵分解及应用