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Variational Approximations between Mean Field Theory and the Junction Tree Algorithm (2000) [25 citations — 1 self]

by Wim Wiegerinck
In Uncertainty in Artificial Intelligence
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Abstract:

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generalised mean field equations to optimise the cluster potentials. We show that the method bridges the gap between the standard mean field approximation and the exact junction tree algorithm. In addition, we address the problem of how to choose the structure and the free parameters of the approximating distribution. From the generalised mean field equations we derive rules to simplify the approximation in advance without affecting the potential accuracy of the model class. We also show how the method fits into some other variational approximations that are currently popular. 1 INTRODUCTION Graphical models, such as Bayesian networks, Markov fields, and Bolt...

Citations

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