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It's reported that GBP improves convergence over loopy BP, but you can similarly improve convergence of loopy BP by running it on larger clusters. (Koller calls it "Cluster Belief Propagation"). Is it really better to have 3 or more region levels, as opposed to two-level (clusters + separators) used in BP? For instance, GBP with extra region levels can't solve any problems exactly that aren't already solvable with cluster belief propagation, as pointed out by Minka. Also, I have one researcher tell me at NIPS tell me that a straightforward implementation of GBP was not competitive on anything besides grids. Even on grids, it's not clear to me that GBP would be better than belief propagation run on overlapping clusters of 2x2 nodes. So my question is, are there any examples where Generalized Belief Propagation with 3 or more region levels would give better results than what can be achieved with cluster BP? |
