John Winn and Christopher M. Bishop
This paper presents Variational Message Passing (VMP), a general purpose algorithm for applying variational inference to a Bayesian Network. Like belief propagation, Variational Message Passing proceeds by passing messages between nodes in the graph and updating posterior beliefs using local operations at each node. Each such update increases a lower bound on the log evidence (unless already at a local maximum). In contrast to belief propagation, VMP can be applied to a very general class of conjugate-exponential models because it uses a factorised variational approximation. Furthermore, by introducing additional variational parameters, VMP can be applied to models containing non-conjugate distributions. The VMP framework also allows the lower bound to be evaluated, and this can be used both for model comparison and for detection of convergence. Variational Message Passing has been implemented in the form of a general purpose inference engine called VIBES (`Variational Inference for BayEsian networkS') which allows models to be specified graphically and then solved variationally without recourse to coding.
In Journal of Machine Learning Research