The Variational Bayes Method in Signal Processing

This is the first book-length treatment of the Variational Bayes (VB) approximation in signal processing. It has been written as a self-contained, self-learning guide for academic and industrial research groups in signal processing, data analysis, machine learning, identification and control. It reviews the VB distributional approximation, showing that tractable algorithms for parametric model identification can be generated in off-line and on-line contexts. Many of the principles are first illustrated via easy-to-follow scalar decomposition problems. In later chapters, successful applications are found in factor analysis for medical image sequences, mixture model identification and speech reconstruction. Results with simulated and real data are presented in detail. The unique development of an eight-step "VB method", which can be followed in all cases, enables the reader to develop a VB inference algorithm from the ground up, for their own particular signal or image model.

Synthesizes the Variational Bayes (VB) method of distributional approximation into eight clear steps ("the VB method"). When these are followed, the reader is equipped with the means to check if their model is amenable to this approximation, and to develop the approximation in a systematic way Presents some very basic toy problems involving scalar decompositions, which give insight into the nature of the method in full applications Employs the VB method in off-line and on-line scenarios in a standard and systematic way, allowing the results in each case to be compared with ease Derives all necessary results in Bayesian methods, avoiding unnecessary elaboration and making the book self-contained

Inhalt
Bayesian Theory.- Off-line Distributional Approximations and the Variational Bayes Method.- Principal Component Analysis and Matrix Decompositions.- Functional Analysis of Medical Image Sequences.- On-line Inference of Time-Invariant Parameters.- On-line Inference of Time-Variant Parameters.- The Mixture-based Extension of the AR Model (MEAR).- Concluding Remarks.