On Mini-Buckets and the Min-fill Elimination Ordering

Abstract

Mini-Bucket Elimination (MBE) is a well-known approximation of Bucket Elimination (BE), deriving bounds on quantities of interest over graphical models. Both algorithms are based on the sequential transformation of the original problem by eliminating variables, one at a time. The order in which variables are eliminated is usually computed using the greedy min-fill heuristic. In the BE case, this heuristic has a clear intuition, because it faithfully represents the structure of the sequence of sub-problems that BE generates and orders the variables using a greedy criteria based on such structure. However, MBE produces a sequence of sub-problems with a different structure. Therefore, using the min-fill heuristic with MBE means that decisions are made using the structure of the sub-problems that BE would produce, which is clearly meaningless. In this paper we propose a modification of the min-fill ordering heuristic that takes into account this fact. Our experiments on a number of benchmarks over two important tasks (i.e., computing the probability of evidence and optimization) show that MBE using the new ordering is often far more accurate than using the standard one.