[edit]

# Convergent Decomposition Solvers for Tree-reweighted Free Energies

*Proceedings of the Fourteenth International Conference on Artificial Intelligence and Statistics*, PMLR 15:388-398, 2011.

#### Abstract

We investigate minimization of tree-reweighted 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 efficient for tree-reweighted energies arising from a small number of spanning trees. While this assumption may seem restrictive at first, 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 embarassingly parallel. In contrast to the original message passing algorithm introduced for this problem, we obtain global convergence guarantees.