2023/02/18 by Jun Lü, Lu, Jun
Computer Science · Mathematics · Physics and Astronomy · #Artificial Intelligence (cs.AI) #Blind Source Separation Techniques #Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Gamma-ray bursts and supernovae #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #Tensor decomposition and applications #and Science (cs.CE)
paper · pdf · doi:10.48550/arxiv.2302.11337
openalex publication_date 2023/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.