Expectation-propagation Algorithms for Linear Regression with Poisson Noise: Application to Photon-limited Spectral Unmixing

This paper discusses Expectation-Propagation (EP) methods for approximate Bayesian inference in the context of linear regression with Poisson noise. We review two main factor graphs used for generalized linear models and discuss how different EP algorithms can be derived. The estimation performance based on EP approximations is compared to the performance using Monte Carlo sampling from the exact posterior distribution. In particular, we observe that using locally independent or isotropic approximate factors enables more robust and scalable algorithms while providing reliable posterior means and marginal variances.