Convergent Decomposition Solvers for Tree-reweighted Free Energies

We investigate minimization of treereweighted free energies for the purpose of obtaining approximate marginal probabilities and upper bounds on the partition function of cyclic graphical models. The solvers we present for this problem work by directly tightening tree-reweighted upper bounds. As a result, they are particularly ecient for tree-reweighted energies arising from a small number of spanning trees. While this assumption may seem restrictive at rst, we show how small sets of trees can be constructed in a principled manner. An appealing property of our algorithms, which results from the problem decomposition, is that they are embarrassingly parallel. In contrast to the original message passing algorithm introduced for this problem, we obtain global convergence guarantees.