Probabilistic Neural Circuits
This work addresses the limitation of tractable probabilistic models for machine learning practitioners by offering a more expressive alternative, though it appears incremental in bridging existing frameworks.
The paper tackles the trade-off between tractability and expressiveness in probabilistic models by introducing probabilistic neural circuits (PNCs), which combine aspects of probabilistic circuits and neural networks, showing they can be interpreted as deep mixtures of Bayesian networks and serve as powerful function approximators in experiments.
Probabilistic circuits (PCs) have gained prominence in recent years as a versatile framework for discussing probabilistic models that support tractable queries and are yet expressive enough to model complex probability distributions. Nevertheless, tractability comes at a cost: PCs are less expressive than neural networks. In this paper we introduce probabilistic neural circuits (PNCs), which strike a balance between PCs and neural nets in terms of tractability and expressive power. Theoretically, we show that PNCs can be interpreted as deep mixtures of Bayesian networks. Experimentally, we demonstrate that PNCs constitute powerful function approximators.