  Networks can describe the structure of a wide variety of complex systems by
specifying which pairs of entities in the system are connected. While such
pairwise representations are flexible, they are not necessarily appropriate
when the fundamental interactions involve more than two entities at the same
time. Pairwise representations nonetheless remain ubiquitous, because
higher-order interactions are often not recorded explicitly in network data.
Here, we introduce a Bayesian approach to reconstruct latent higher-order
interactions from ordinary pairwise network data. Our method is based on the
principle of parsimony and only includes higher-order structures when there is
sufficient statistical evidence for them. We demonstrate its applicability to a
wide range of datasets, both synthetic and empirical.
