Reviews: Probabilistic Inference with Generating Functions for Poisson Latent Variable Models

The idea of probability generating function achieving similar forms of "conjugacy" as Gaussian random variables and (finite) discrete random variables is very interesting. This enables a fast and exact inference algorithm on Poisson latent variable models. The formulation involving probability generating function does not seem to be constrained to Poisson random variables but all the simulations and real application pertain to Poisson HMM. It is unclear if there's anything special with Poisson that enables better parameter estimates. It is also unclear if there are other Poisson latent variable models other than Poisson HMMs with wide applications.