Neural Cluster Tree Elimination

We introduce Neural Cluster Tree Elimination (NCTE), a method for approximate probabilistic inference over discrete graphical models. The scheme approximates hard-to-compute messages over tree decompositions of the graphical model using neural networks. It extends Neural Bucket Elimination (NeuroBE)—an earlier approach restricted to bucket trees and to the bucket elimination scheme. By merging buckets into clusters, NCTE replaces a long chain of neural approximators with fewer networks, improving efficiency by requiring fewer networks to be trained and boosting accuracy by reducing error accumulation. We provide several strategies for transitioning from a bucket tree to a cluster tree to optimize the tradeoff between time and accuracy. Our empirical evaluation demonstrates the benefits and competitiveness of this approach for computing the partition function of a graphical model.