Revisiting the Decomposition Approach to Inference in Exponential Families and Graphical Models

The approach to upper-bounding the (log-)partition function and the modes of a probability distribution from a general exponential family is revisited. This approach is based on decomposition of the original problem into tractable subproblems. It was proposed by Wainwright et al. for undirected graphical models (MRFs) and tree-structured subproblems. We generalize it to general subproblems and general exponential families.