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 pair-wise models can be reparametrized so that existing convergent algorithms for lifted marginal inference can be used without modification.
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