Abstract
Sum-product networks (SPNs) are a deep learning model that have shown impressive results in several artificial intelligence applications. Tractable inference in practice requires an SPN to be complete and either consistent or decomposable. These properties can be verified using the definition of scope. In fact, the notion of scope can be used to define SPNs when they are interpreted as hierarchically structured latent variables in mixture models.
In this paper, we first show that the mixture model definition of scope is inconsistent with interpreting SPNs as arithmetic circuit (ACs), the network on which SPNs were founded. We then propose a definition of scope that is consistent with an AC interpretation. We next show that the AC definition of scope can be used for verifying the completeness property of SPNs, but not for verifying consistency or decomposability, nor is it consistent with a mixture model interpretation. We resolve the above inconsistencies by presenting a more general definition of scope that remains suitable for both AC and mixture model interpretations of SPNs, and can also be used for verifying the complete, consistent, and decomposable properties of SPNs.
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Oliveira, J.S., Butz, C.J., dos Santos, A.E. (2017). Resolving Inconsistencies of Scope Interpretations in Sum-Product Networks. In: Mouhoub, M., Langlais, P. (eds) Advances in Artificial Intelligence. Canadian AI 2017. Lecture Notes in Computer Science(), vol 10233. Springer, Cham. https://doi.org/10.1007/978-3-319-57351-9_35
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DOI: https://doi.org/10.1007/978-3-319-57351-9_35
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