Negative Tree Reweighted Belief Propagation
This offers a theoretical advance for probabilistic inference in graphical models, though it appears incremental as it extends prior tree-reweighted belief propagation work.
The paper tackles the problem of approximating the log partition function of Markov random fields by introducing a new class of lower bounds using a reversed Jensen's inequality and linear combinations of spanning trees with negative weights, providing a counterpart to existing upper-bound methods.
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen's inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound counterpart to the tree-reweighted belief propagation algorithm, which uses a convex combination of spanning trees with positive weights to provide corresponding upper bounds. We develop algorithms to optimize and tighten the lower bounds over the non-convex set of valid parameter values. Our algorithm generalizes mean field approaches (including naive and structured mean field approximations), which it includes as a limiting case.