Before revision:  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. In this work, we provide tight information-theoretic upper and lower bounds for the recovery problem , as well as the first non-trivial algorithmic bounds based on approximate message passing algorithms.
After revision:  We first observe that it can be viewed as a structural variant of tensor-PCA problem. We provide tight upper and lower bounds for the recovery problem , as well as the first non-trivial algorithmic bounds based on approximate message passing algorithms.