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A Class of Random Fields on Complete Graphs with Tractable Partition Function
Sept. 2013 (vol. 35 no. 9)
pp. 2304-2306
B. Flach, Fac. of Electr. Eng., Czech Tech. Univ., Prague, Czech Republic
The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary potentials. Similarly, the partition function and marginal probabilities can be computed in polynomial time for random fields on complete bipartite graphs, provided they have homogeneous pairwise potentials. We expect that these tractable classes of large-scale random fields can be very useful for the evaluation of approximation algorithms by providing exact error estimates.
Index Terms:
probability,approximation theory,computational complexity,graph theory,error estimation,random field,tractable partition function,marginal probability,polynomial time complexity,homogeneous pairwise potential,complete bipartite graph,approximation algorithm,Labeling,Computational modeling,Bipartite graph,Partitioning algorithms,Time complexity,Approximation methods,Polynomials,Markov random fields
Citation:
B. Flach, "A Class of Random Fields on Complete Graphs with Tractable Partition Function," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 9, pp. 2304-2306, Sept. 2013, doi:10.1109/TPAMI.2013.99
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