# Principled and Efficient Motif Finding for Structure Learning of Lifted Graphical Models

arXiv: https://arxiv.org/abs/2302.04599 · HTML: https://mlsanity.com/paper/2302.04599/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 49 references that are in the map.
- First posted on arXiv 9 Feb 2023.

## Builds on (most cited first, 12 of 12)

- [Neural Probabilistic Logic Programming in DeepProbLog](https://mlsanity.com/paper/1907.08194/) (2019)
- [Learning Explanatory Rules from Noisy Data](https://mlsanity.com/paper/1711.04574/) (2017)
- [DRUM: End-To-End Differentiable Rule Mining On Knowledge Graphs](https://mlsanity.com/paper/1911.00055/) (2019)
- [End-to-End Differentiable Proving](https://mlsanity.com/paper/1705.11040/) (2017)
- [Go for a Walk and Arrive at the Answer: Reasoning Over Paths in Knowledge Bases using Reinforcement Learning](https://mlsanity.com/paper/1711.05851/) (2017)
- [Harnessing Deep Neural Networks with Logic Rules](https://mlsanity.com/paper/1603.06318/) (2016)
- [Hinge-Loss Markov Random Fields and Probabilistic Soft Logic](https://mlsanity.com/paper/1505.04406/) (2015)
- [Traversing Knowledge Graphs in Vector Space](https://mlsanity.com/paper/1506.01094/) (2015)
- [Best-Effort Inductive Logic Programming via Fine-grained Cost-based Hypothesis Generation](https://mlsanity.com/paper/1707.02729/) (2017)
- [Towards Neural Theorem Proving at Scale](https://mlsanity.com/paper/1807.08204/) (2018)
- [Deep Probabilistic Logic: A Unifying Framework for Indirect Supervision](https://mlsanity.com/paper/1808.08485/) (2018)
- [Semantic Width and the Fixed-Parameter Tractability of Constraint Satisfaction Problems](https://mlsanity.com/paper/2007.14169/) (2020)

## Built on by (most cited first, 4 of 4)

- [On Learning Latent Models with Multi-Instance Weak Supervision](https://mlsanity.com/paper/2306.13796/) (2023)
- [Parallel Neurosymbolic Integration with Concordia](https://mlsanity.com/paper/2306.00480/) (2023)
- [Efficiently Learning Probabilistic Logical Models by Cheaply Ranking Mined Rules](https://mlsanity.com/paper/2409.16238/) (2024)
- [Neuro-symbolic Weak Supervision: Theory and Semantics](https://mlsanity.com/paper/2503.18509/) (2025)

## Abstract (arXiv)

Structure learning is a core problem in AI central to the fields of neuro-symbolic AI and statistical relational learning. It consists in automatically learning a logical theory from data. The basis for structure learning is mining repeating patterns in the data, known as structural motifs. Finding these patterns reduces the exponential search space and therefore guides the learning of formulas. Despite the importance of motif learning, it is still not well understood. We present the first principled approach for mining structural motifs in lifted graphical models, languages that blend first-order logic with probabilistic models, which uses a stochastic process to measure the similarity of entities in the data. Our first contribution is an algorithm, which depends on two intuitive hyperparameters: one controlling the uncertainty in the entity similarity measure, and one controlling the softness of the resulting rules. Our second contribution is a preprocessing step where we perform hierarchical clustering on the data to reduce the search space to the most relevant data. Our third contribution is to introduce an O(n ln n) (in the size of the entities in the data) algorithm for clustering structurally-related data. We evaluate our approach using standard benchmarks and show that we outperform state-of-the-art structure learning approaches by up to 6% in terms of accuracy and up to 80% in terms of runtime.