Linear-time rule mining under formal guarantees

Probabilistic logical models are a core component of neurosymbolic AI and are important in their own right for tasks that require high explainability. Unlike neural networks, logical theories that underlie the model are often handcrafted using domain expertise, making their development costly and prone to errors. While there are algorithms that learn logical theories from data, they are generally prohibitively expensive, limiting their applicability in real-world settings. Here, we introduce precision and recall for logical rules and define their composition as rule utility -- a measure of the predictive power of logical theories that can be computed in linear time. We then present SPECTRUM, a linear-time framework for learning logical theories from relational data, that mines recurrent patterns in the data, and subsequently, using our utility measure, evaluates and ranks rules derived from these patterns. Finally, we prove theoretical guarantees on the utility of the learnt logical theory. As a result, we demonstrate across various tasks that SPECTRUM scales to larger datasets, often learning more accurate logical theories on CPUs in < 1% of the runtime of SOTA neural network approaches on GPUs.