Deep probabilistic circuits for efficient uncertainty handling in learning systems

Abstract Probabilistic modeling lies at the core of machine learning, providing a principled framework to represent and reason about uncertainty. Probabilistic circuits (PCs) have emerged as a class of models that balance representational power with computational efficiency via a deep probabilistic architecture that enables tractable uncertainty handling. This paper provides an overview of PCs as deep and efficient probabilistic models, highlighting their ability to encode complex distributions while maintaining computational guarantees for key inference tasks. We first introduce the foundations of tractable probabilistic modeling with PCs, elaborating on how they represent and handle uncertainty, and the different approaches for structure and parameter learning. We then review successful applications and enhancements, with particular emphasis on recent advances in time series modeling and forecasting, where PCs demonstrate state-of-the-art accuracy while being robust and efficient. Furthermore, we discuss a tractable method to estimate epistemic uncertainty, which is particularly helpful in improving the PCs’ robustness when they are faced with real-world out-of-distribution instances, and provide additional results on the task of time series classification. The paper concludes with a perspective on open challenges and future research directions, including scaling to high-dimensional data, the hybridization with neural architectures, and the transformation and connection with other non-probabilistic models. Overall, this paper examines and underscores the role of PCs as a central approach within probabilistic modeling, pointing out their strengths, limitations, and potential avenues for further development.