Sum-Product Network Decompilation

Abstract: There exists a dichotomy between classical probabilistic graphical models, such as Bayesian networks (BNs), and modern tractable models, such as sum-product networks (SPNs). The former generally have intractable inference, but provide a high level of interpretability, while the latter admits a wide range of tractable inference routines, but are typically harder to interpret. Due to this dichotomy, tools to convert between BNs and SPNs are desirable. While one direction -- compiling BNs into SPNs -- is well discussed in Darwiche's seminal work on arithmetic circuit compilation, the converse direction -- decompiling SPNs into BNs -- has received surprisingly little attention. In this paper, we fill this gap by proposing SPN2BN, an algorithm that decompiles an SPN into a BN. SPN2BN has several salient features when compared to the only other two works decompiling SPNs. Most significantly, the BNs returned by SPN2BN are minimal independence-maps that are more parsimonious with respect to the introduction of latent variables. Secondly, the output BN produced by SPN2BN can be precisely characterized with respect to a compiled BN. More specifically, a certain set of directed edges will be added to the input BN, giving what we will call the moral-closure. Lastly, it is established that our compilation-decompilation process is idempotent. This has practical significance as it limits the size of the decompiled SPN.