Lifted Tree-Reweighted Variational Inference
This work addresses computational efficiency in probabilistic inference for symmetric models, representing an incremental improvement over existing lifted belief propagation methods.
The paper tackles variational inference for symmetric graphical models from first-order probabilistic models by developing a lifted tree-reweighted formulation that is more efficient than standard approaches and provides an upper bound on the partition function. It introduces methods to improve this bound through optimized edge appearance probabilities and tightened constraints using lifted cycle inequalities and exchangeable cluster consistency.
We analyze variational inference for highly symmetric graphical models such as those arising from first-order probabilistic models. We first show that for these graphical models, the tree-reweighted variational objective lends itself to a compact lifted formulation which can be solved much more efficiently than the standard TRW formulation for the ground graphical model. Compared to earlier work on lifted belief propagation, our formulation leads to a convex optimization problem for lifted marginal inference and provides an upper bound on the partition function. We provide two approaches for improving the lifted TRW upper bound. The first is a method for efficiently computing maximum spanning trees in highly symmetric graphs, which can be used to optimize the TRW edge appearance probabilities. The second is a method for tightening the relaxation of the marginal polytope using lifted cycle inequalities and novel exchangeable cluster consistency constraints.