On Properties of the Minimum Entropy Sub-tree to Compute Lower Bounds on the Partition Function

— Computing the partition function and the marginals of a global probability distribution are two important issues in any probabilistic inference problem. In a previous work, we presented sub-tree based upper and lower bounds on the partition function of a given probabilistic inference problem. Using the entropies of the sub-trees we proved an inequality that compares the lower bounds obtained from different sub-trees. In this paper we investigate the properties of one specific lower bound, namely the lower bound computed by the minimum entropy sub-tree. We also investigate the relationship between the minimum entropy sub-tree and the sub-tree that gives the best lower bound.

• Type: Journal
• Year: 2011
• Where: CORR
• Authors: Mehdi Molkaraie, Payam Pakzad
• Keywords: CORR 2011, Education, Lower Bound, Minimum Entropy Sub-tree, Probabilistic Inference Problem