Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules

Jonathan Feldstein, Dominic Phillips, Efthymia Tsamoura

Keywords: Structure Learning, Probabilistic Logical Models, MLN, PSL, Knowledge Graph Reasoning, Neurosymbolic

TL;DR: We introduce a framework that efficiently learns logical rules from data, using a linear-time algorithm to mine recurrent structures in the data and a cheap proxy to evaluate the predictive power of logical models.

Abstract: Probabilistic logical models are a core component of neurosymbolic AI and are important models in their own right for tasks that require high explainability. Unlike neural networks, logical models are often handcrafted using domain expertise, making their development costly and prone to errors. While there are algorithms that learn logical models from data, they are generally prohibitively expensive, limiting their applicability in real-world settings. In this work, we introduce precision and recall for logical rules and define their composition as rule utility -- a cost-effective measure to evaluate the predictive power of logical models. Further, we introduce SPECTRUM, a scalable framework for learning logical models from relational data. Its scalability derives from a linear-time algorithm that mines recurrent structures in the data along with a second algorithm that, using the cheap utility measure, efficiently ranks rules built from these structures. Moreover, we derive theoretical guarantees on the utility of the learnt logical model. As a result, we demonstrate across various tasks that SPECTRUM scales to larger datasets, often learning more accurate logical models orders of magnitude faster than previous methods without requiring specialised GPU hardware.

Primary Area: neurosymbolic & hybrid AI systems (physics-informed, logic & formal reasoning, etc.)

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Submission Number: 3632