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# Conditional Sum-Product Networks: Imposing Structure on Deep Probabilistic Architectures

*Proceedings of the 10th International Conference on Probabilistic Graphical Models*, PMLR 138:401-412, 2020.

#### Abstract

Probabilistic graphical models are a central tool in AI, however, they are generally not as expressive
as deep neural models, and inference is notoriously hard and slow. In contrast, deep probabilistic
models such as sum-product networks (SPNs) capture joint distributions in a tractable fashion,
but still lack the expressive power of intractable models based on deep neural networks. Therefore,
we introduce conditional SPNs (CSPNs), conditional density estimators for multivariate and
potentially hybrid domains that allow harnessing the expressive power of neural networks while
still maintaining tractability guarantees. One way to implement CSPNs is to use an existing SPN
structure and condition its parameters on the input, e.g., via a deep neural network. Our experimental
evidence demonstrates that CSPNs are competitive with other probabilistic models and yield
superior performance on multilabel image classification compared to mean field and mixture density
networks. Furthermore, they can successfully be employed as building blocks for structured
probabilistic models, such as autoregressive image models.