An Arithmetic Circuit (AC) is a deep learning probabilistic model that is compiled by eliminating every variable in a given Bayesian Network (BN). We introduce a special case of AC, called a p-AC, in which every node is a 1, marginal, or conditional of the joint distribution defined by the given BN. This is accomplished by using wait-sets to restrict the elimination ordering used. We show both theoretical and practical advantages of p-ACs over ACs, including that there is no increase in network size. Lastly, we observe and analyze an interesting graphical relationship between semantics in deep learning inference and causal analysis.
Article ID: 2023L17
Publisher: Canadian Artificial Intelligence Association