  We show how to use a variational approximation to the logistic function to
perform approximate inference in Bayesian networks containing discrete nodes
with continuous parents. Essentially, we convert the logistic function to a
Gaussian, which facilitates exact inference, and then iteratively adjust the
variational parameters to improve the quality of the approximation. We
demonstrate experimentally that this approximation is faster and potentially
more accurate than sampling. We also introduce a simple new technique for
handling evidence, which allows us to handle arbitrary distributions on
observed nodes, as well as achieving a significant speedup in networks with
discrete variables of large cardinality.
