Probabilistic Neural Circuits

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. 1. We introduce conditional probabilistic circuits, from which we construct probabilistic neural circuits (PNCs), which we interpret as deep mixtures of Bayesian nets. 2. We provide a prescription to construct layered PNCs. 3. We provide an implementation of layered PNCs and experimentally study their expressive power. Our work is influenced by that of Sharir and Shashua (2018). We discuss the relationship to their approach (dubbed sum-product-quotient networks) in Section 5.