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.

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

Exact inference in probabilistic graphical models is particularly challenging in the presence of relational and other deterministic constraints. For discrete domains, weighted model counting has emerged as an effective and general approach in a variety of formalisms, and lifted reasoning has pushed the envelope further in exploiting symmetry properties over indistinguishable groups of objects, thereby avoiding the need to perform inference on the exponential ground theory.

Jonathan Feldstein

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