Graphical models with latent count variables arise in a number of fields. Standard exact inference techniques such as variable elimination and belief propagation do not apply to these models because the latent variables have countably infinite support. As a result, approximations such as truncation or MCMC are employed. We present the first exact inference algorithms for a class of models with latent count variables by developing a novel representation of countably infinite factors as probability generating functions, and then performing variable elimination with generating functions. Our approach is exact, runs in pseudo-polynomial time, and is much faster than existing approximate techniques. It leads to better parameter estimates for problems in population ecology by avoiding error introduced by approximate likelihood computations.
Recommended citation: Kevin Winner and Daniel Sheldon. Probabilistic inference with generating functions for Poisson latent variable models. In Advances in Neural Information Processing Systems 30, 2016 http://kwinner.github.io/files/WinnerSheldon2016.pdf