Towards Inference in Arithmetic Circuits by Exploiting Barren Variables

Arithmetic circuits (ACs) have been empirically shown to be the state-of-the-art method for exact inference in discrete Bayesian networks (BNs). Although ACs are a compact and efficient computational model, they do not perform any optimization steps for a given query. Here, we introduce AC inference that exploits barren variables, a standard optimization step when conducting probabilistic inference directly within the BN itself. The main idea is to compute an AC node's value only if that node is relevant to a given query. Our experimental results on ACs compiled from well-known and randomly generated BNs evaluate the effectiveness of barren variable exploitation across varying elimination orders, query sizes, and query types. While the results are somewhat mixed, this work is the first to demonstrate AC inference without requiring probability propagation over the entire circuit and paves the way for future improvements.