Methods for constructing balanced elimination trees and other recursive decompositions

An elimination tree is a form of recursive factorization for Bayesian networks. Elimination trees can be used as the basis for a practical implementation of Bayesian network inference via conditioning graphs. The time complexity for inference in elimination trees has been shown to be O(nexp(d)), where d is the height of the elimination tree. In this paper, we demonstrate two new heuristics for building small elimination trees. We also demonstrate a simple technique for deriving elimination trees from Darwiche et al.’s dtrees, and vice versa. We show empirically that our heuristics, combined with a constructive process for building elimination trees, produces the smaller elimination trees than previous methods.