  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.
