Stable Belief Propagation in Gaussian Dags

We consider approximate inference in the important class of Gaussian distributions corresponding to multiply-connected directed acylic networks (DAGs). We show how directed belief propagation can be implemented in a numerically stable manner by associating backward (λ) messages with an auxiliary variable, enabling intermediate computations to be carried out in moment form. We apply our method to the fast Fourier transform network with missing data, and show that the results are more accurate than those obtained using undirected belief propagation on the equivalent Markov network.