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

TL;DR

This paper introduces a novel, principled method for mining structural motifs in lifted graphical models, significantly improving the efficiency and accuracy of structure learning in probabilistic logical models.

Contribution

It presents the first principled algorithm for motif mining in lifted models, incorporating a stochastic similarity measure, hierarchical clustering, and an efficient O(n ln n) clustering algorithm.

Findings

Outperforms state-of-the-art in accuracy by up to 6%.

Reduces runtime by up to 80%.

Effectively identifies structural motifs in benchmark datasets.

Abstract

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.