Recovery a planted signal perturbed by noise is a fundamental problem in machine learning. In this work, we consider the problem of recovery a planted k-densest sub-hypergraph on h-uniform hypergraphsover n nodes . 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. 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. The problem exhibits a typical information-to-computational-gap observed in analogous settings, that widens with increasing sparsity of the problem. Interestingly, the bounds show that the structure of the signal does have an impact on the existing bounds of tensor PCA that the unstructured planted signal does not capture .
 In this work, we consider the problem of recovery a planted k-densest sub-hypergraph on d-uniform hypergraphs . This fundamental problem appears in different contexts, e.g., community detection, average-case complexity, and neuroscience applications as a structural variant of tensor-PCA problem. We provide tightinformation-theoretic upper and lower bounds for the exact recovery threshold by the maximum-likelihood estimator , as well as algorithmic bounds based on approximate message passing algorithms. The problem exhibits a typical statistical-to-computational gap observed in analogous sparse settings that widen with increasing sparsity of the problem. The bounds show that the signal structure impacts the location of the statistical and computational phase transition that the known existing bounds for the tensor-PCA model do not capture. This effect is due to the generic planted signal prior that this latter model addresses .
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Recovery a planted signal perturbed by noise is a fundamental problem in machine learning.
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h-uniform hypergraphsover n nodes
d-uniform hypergraphs
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average case
average-case
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. We first observe that it can be viewed
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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
tensor-PCA problem. We provide tight
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information-theoretic
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recovery problem
exact recovery threshold by the maximum-likelihood estimator
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the first non-trivial algorithmic
algorithmic
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information-to-computational-gap
statistical-to-computational gap
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settings, that widens
sparse settings that widen
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Interestingly, the
The
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structure of the signal does have an impact on the existing bounds of tensor PCA that the unstructured planted signal does not capture
signal structure impacts the location of the statistical and computational phase transition that the known existing bounds for the tensor-PCA model do not capture. This effect is due to the generic planted signal prior that this latter model addresses