Beyond Log-Supermodularity: Lower Bounds and the Bethe Partition Function
A recent result has demonstrated that the Bethe partition function always lower bounds the true partition function of binary, log-supermodular graphical models. We demonstrate that these results can be extended to other interesting classes of graphical models that are not necessarily binary or log-supermodular: the ferromagnetic Potts model with a uniform external field and its generalizations and special classes of weighted graph homomorphism problems.
PDF Link: /papers/13/p546-ruozzi.pdf
AUTHOR = "Nicholas Ruozzi
TITLE = "Beyond Log-Supermodularity: Lower Bounds and the Bethe Partition Function",
BOOKTITLE = "Proceedings of the Twenty-Ninth Conference Annual Conference on Uncertainty in Artificial Intelligence (UAI-13)",
PUBLISHER = "AUAI Press",
ADDRESS = "Corvallis, Oregon",
YEAR = "2013",
PAGES = "546--555"