Equitable Partitions of Concave Free EnergiesMartin Mladenov; Kristian Kersting
In: Marina Meila; Tom Heskes (Hrsg.). Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence. Conference in Uncertainty in Artificial Intelligence (UAI-2015), July 12-16, Amsterdam, Netherlands, Pages 602-611, AUAI Press, 2015.
Significant progress has recently been made towards formalizing symmetry-aware variational inference approaches into a coherent framework. With the exception of TRW for marginal inference, however, this framework resulted in approximate MAP algorithms only, based on equitable and orbit partitions of the graphical model. Here, we deepen our understanding of it for marginal inference. We show that a large class of concave free energies admits equitable partitions, of which orbit partitions are a special case, that can be exploited for lifting. Although already interesting on its own, we go one step further. We demonstrate that concave free energies of pairwise models can be reparametrized so that existing convergent algorithms for lifted marginal inference can be used without modification.