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MPRM: A Markov Path-based Rule Miner for Efficient and Interpretable Knowledge Graph Reasoning

Mingyang Li, Song Wang, Ning Cai

TL;DR

MPRM reframes rule-based reasoning for knowledge graphs as a Markov chain, introducing a path-probability aggregation confidence (PRM) to enable efficient, interpretable rule mining. By mining a concise set of connected and closed Horn rules and evaluating them via a Markov-based confidence measure, MPRM achieves competitive link prediction performance with minimal data sampling, even on graphs with millions of facts, using a standard CPU. The approach combines Bi-BFS-derived rule extraction, probabilistic reasoning, and top-K rule aggregation to deliver transparent, rule-based explanations while maintaining scalability. Experimental results on FB15K-237, WN18RR, YAGO3-10, and NELL-995 demonstrate strong interpretability, superior efficiency, and robust accuracy advantages over baselines, including traditional rule miners and some neural approaches. The work suggests a practical pathway toward scalable, interpretable KG reasoning suitable for resource-constrained environments and real-world applications.

Abstract

Rule mining in knowledge graphs enables interpretable link prediction. However, deep learning-based rule mining methods face significant memory and time challenges for large-scale knowledge graphs, whereas traditional approaches, limited by rigid confidence metrics, incur high computational costs despite sampling techniques. To address these challenges, we propose MPRM, a novel rule mining method that models rule-based inference as a Markov chain and uses an efficient confidence metric derived from aggregated path probabilities, significantly lowering computational demands. Experiments on multiple datasets show that MPRM efficiently mines knowledge graphs with over a million facts, sampling less than 1% of facts on a single CPU in 22 seconds, while preserving interpretability and boosting inference accuracy by up to 11% over baselines.

MPRM: A Markov Path-based Rule Miner for Efficient and Interpretable Knowledge Graph Reasoning

TL;DR

MPRM reframes rule-based reasoning for knowledge graphs as a Markov chain, introducing a path-probability aggregation confidence (PRM) to enable efficient, interpretable rule mining. By mining a concise set of connected and closed Horn rules and evaluating them via a Markov-based confidence measure, MPRM achieves competitive link prediction performance with minimal data sampling, even on graphs with millions of facts, using a standard CPU. The approach combines Bi-BFS-derived rule extraction, probabilistic reasoning, and top-K rule aggregation to deliver transparent, rule-based explanations while maintaining scalability. Experimental results on FB15K-237, WN18RR, YAGO3-10, and NELL-995 demonstrate strong interpretability, superior efficiency, and robust accuracy advantages over baselines, including traditional rule miners and some neural approaches. The work suggests a practical pathway toward scalable, interpretable KG reasoning suitable for resource-constrained environments and real-world applications.

Abstract

Rule mining in knowledge graphs enables interpretable link prediction. However, deep learning-based rule mining methods face significant memory and time challenges for large-scale knowledge graphs, whereas traditional approaches, limited by rigid confidence metrics, incur high computational costs despite sampling techniques. To address these challenges, we propose MPRM, a novel rule mining method that models rule-based inference as a Markov chain and uses an efficient confidence metric derived from aggregated path probabilities, significantly lowering computational demands. Experiments on multiple datasets show that MPRM efficiently mines knowledge graphs with over a million facts, sampling less than 1% of facts on a single CPU in 22 seconds, while preserving interpretability and boosting inference accuracy by up to 11% over baselines.
Paper Structure (32 sections, 10 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 32 sections, 10 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminary
  3. Horn rules and Confidence metric
  4. Problem Formulation
  5. Binary Horn Rules
  6. Rule Confidence
  7. Markov-Based Confidence Measure
  8. State Space
  9. Transition Probabilities
  10. Rule Confidence via Path Probability Aggregation
  11. Mechanism Analysis
  12. Markov Path-based Rule Miner
  13. Rule Extraction
  14. Reasoning
  15. Time Complexity Analysis
  16. ...and 17 more sections

Figures (4)

  • Figure 1: Rule extraction and reasoning framework. The extracted rule $r_1(x, z_1)$$\land r_2(z_1, y)$$\implies r(x, y)$ resolves the query $(s,r,?)$, where $Q(s,r)=\{o\}$. The numerical values annotated on each node represent the probability of reaching the corresponding node at time step $t$.
  • Figure 2: Ablation study on path probability.
  • Figure 3: AnyBURL runs for 100 seconds and MPRM for 26 seconds, after which each selects the $K$ rules with the highest confidence for link prediction.
  • Figure 4: As $\alpha$ varies from 1 to infinity with other hyperparameter held constant. The result on three datasets show that each relation requires only a small number of facts to achieve the accuracy of learning all facts, highlighting the efficiency of MPRM.