  Network motifs are recurrent, small-scale patterns of interactions observed
frequently in a system. They shed light on the interplay between the topology
and the dynamics of complex networks across various domains. In this work, we
focus on the problem of counting occurrences of small sub-hypergraph patterns
in very large hypergraphs, where higher-order interactions connect arbitrary
numbers of system units. We show how directly exploiting higher-order
structures speeds up the counting process compared to traditional data mining
techniques for exact motif discovery. Moreover, with hyperedge sampling,
performance is further improved at the cost of small errors in the estimation
of motif frequency. We evaluate our method on several real-world datasets
describing face-to-face interactions, co-authorship and human communication. We
show that our approximated algorithm allows us to extract higher-order motifs
faster and on a larger scale, beyond the computational limits of an exact
approach.
