  Global variational approximation methods in graphical models allow efficient
approximate inference of complex posterior distributions by using a simpler
model. The choice of the approximating model determines a tradeoff between the
complexity of the approximation procedure and the quality of the approximation.
In this paper, we consider variational approximations based on two classes of
models that are richer than standard Bayesian networks, Markov networks or
mixture models. As such, these classes allow to find better tradeoffs in the
spectrum of approximations. The first class of models are chain graphs, which
capture distributions that are partially directed. The second class of models
are directed graphs (Bayesian networks) with additional latent variables. Both
classes allow representation of multi-variable dependencies that cannot be
easily represented within a Bayesian network.
