A Unified Bayesian Inference Framework for Generalized Linear Models

Abstract

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 (VAMP), and sparse Bayesian learning (SBL). It is proved that the resultant GLM version of AMP is equivalent to the well-known generalized approximate message passing (GAMP). Numerical results for 1-bit quantized compressed sensing (CS) demonstrate the effectiveness of this unified framework.

6 pages,4 figures. To appear in IEEE Signal Processing Letters. This version contains an appendix

References in corpus (4)

• Probabilistic Reconstruction in Compressed Sensing: Algorithms, Phase Diagrams, and Threshold Achieving Matrices
• Turbo Compressed Sensing with Partial DFT Sensing Matrix
• Denoising based Vector Approximate Message Passing
• D-OAMP: A Denoising-based Signal Recovery Algorithm for Compressed Sensing

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