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# Sum-Product Network Decompilation

*Proceedings of the 10th International Conference on Probabilistic Graphical Models*, PMLR 138:53-64, 2020.

#### 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 admit a wide range of tractable inference routi nes, 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.