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 can­ not be done analytically are done using Gaus­ sian 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 similar­ ities with particle filtering algorithms. We discuss these, and also discuss the rela­ tionship with variational Bayes and Laplace propagation. Experimental results are given for an interesting model from mathematical finance.