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

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