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

TL;DR

This paper explores the properties of the minimum entropy sub-tree used to compute lower bounds on the partition function, enhancing understanding of probabilistic inference bounds.

Contribution

It investigates the properties of the minimum entropy sub-tree and its relation to the sub-tree providing the best lower bound in probabilistic inference.

Findings

Analyzes the properties of the minimum entropy sub-tree.

Establishes relationships between different sub-trees and their bounds.

Abstract

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.