Gaussian quadrature based expectation propagation.
We present a general approximation method for Bayesian inference problems. The method is based on Expectation Propagation (EP). Projection steps in the EP iteration that cannot be done analytically are done using Gaussian quadrature. By identifying a general form in the projections, the only quadrature rules that are required are for exponential family weight functions. The corresponding cumulant and moment generating functions can then be used to automatically derive the necessary quadrature rules. In this article the approach is restricted to approximating families that factorize to a product of one-dimensional families. The final algorithm has interesting similarities with particle filtering algorithms. We discuss these, and also discuss the relationship with variational Bayes and Laplace propagation. Experimental results are given for an interesting model from mathematical finance.