Before revision:  This fundamental problem appears in different contexts, e.g., community detection, average case complexity, and neuroscience applications . We first observe that it can be viewed as a structural variant of tensor PCA in which the hypergraph parameters k and h determine the structure of the signal to be recovered when the observations are contaminated by Gaussian noise.
After revision:  This fundamental problem appears in different contexts, e.g., community detection, average case complexity, and neuroscience applications as a structural variant of tensor PCA in which the hypergraph parameters k and h determine the structure of the signal to be recovered when the observations are contaminated by Gaussian noise.