  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.
