A Unified Bayesian Inference Framework for Generalized Linear Models

• Published in: IEEE signal processing letters Vol. 25; no. 3; pp. 398 - 402
• Main Authors: Meng, Xiangming, Wu, Sheng, Zhu, Jiang
• Format: Journal Article
• Language: English
• Published: IEEE 01.03.2018
• Subjects: Approximate message passing (AMP); Approximation algorithms; Bayes methods; Compressed sensing; compressed sensing (CS); generalized linear models (GLM); Inference algorithms; Message passing; Sea measurements; Signal processing algorithms; sparse Bayesian learning (SBL); vector approximate message passing (VAMP)
• ISSN: 1070-9908; 1558-2361
• DOI: 10.1109/LSP.2017.2789163

In this letter, we present a unified Bayesian inference framework for generalized linear models (GLM), which iteratively reduces the GLM problem to a sequence of standard linear model (SLM) problems. This framework provides new perspectives on some established GLM algorithms derived from SLM ones and also suggests novel extensions for some other SLM algorithms. Specific instances elucidated under such framework are the GLM versions of approximate message passing (AMP), vector AMP, and sparse Bayesian learning. It is proved that the resultant GLM version of AMP is equivalent to the well-known generalized approximate message passing. Numerical results for one-bit quantized compressed sensing demonstrate the effectiveness of this unified framework.