Rule Induction in Knowledge Graphs Using Linear Programming

Abstract

Knowledge graph (KG) completion is a well-studied problem in AI. Rule-based methods and embedding-based methods form two of the solution techniques. Rule-based methods learn first-order logic rules that capture existing facts in an input graph and then use these rules for reasoning about missing facts. A major drawback of such methods is the lack of scalability to large datasets. In this paper, we present a simple linear programming (LP) model to choose rules from a list of candidate rules and assign weights to them. For smaller KGs, we use simple heuristics to create the candidate list. For larger KGs, we start with a small initial candidate list, and then use standard column generation ideas to add more rules in order to improve the LP model objective value. To foster interpretability and generalizability, we limit the complexity of the set of chosen rules via explicit constraints, and tune the complexity hyperparameter for individual datasets. We show that our method can obtain state-of-the-art results for three out of four widely used KG datasets, while taking significantly less computing time than other popular rule learners including some based on neuro-symbolic methods. The improved scalability of our method allows us to tackle large datasets such as YAGO3-10.

Neurosymbolic AI for Reasoning on Graph Structures: A Survey

“…• NeuralLP [162] • DRUM [127] • LPRules [33] • RuLES [66] Path-Based Rule Learning (NEURO;SYMBOLIC / NEURO:SYMBOLIC → NEURO)…”

“…• PoLo [89] • LPRules [33] • LNN-MP [134] • RNNLogic [118] • Transductive Augmentation [65] Fig. 1: Taxonomy of neurosymbolic approaches for graph reasoning.…”

“…In contrast, the authors of LPRules [33] take a slightly different approach to learning rules and confidences simultaneously. Their approach generates a weighted combination of logical rules for link prediction by iteratively augmenting a small starter pool of candidate rules.…”

“…Their approach generates a weighted combination of logical rules for link prediction by iteratively augmenting a small starter pool of candidate rules. It differs from the aforementioned methods which learn confidences for the entire set of possible rules because it only works with a subset of rules at any given time, thereby reducing the search space and optimizing the time it takes to find a set of rules which are highly predictive [33]. Another method, RuLES [66], operates very similarly, augmenting its rule set iterativey by constructing and extending rules with additional atoms and logical refinement operators.…”

“…For rule generation regarding a specific relation, such as drug indications in the PoLo study, it iterates through instances of that relation and finds the shortest path between each respective pair of nodes, excluding the current direct edge. From the shortest path, a rule is generated based on its general sequence of relations (which PoLo called a metapath) [33]. From the aforementioned studies, we can see that KGC can depend heavily upon information beyond a node's local neighborhood.…”