Statistical and computational thresholds for the planted k-densest sub-hypergraph problem
Luca Corinzia, Paolo Penna, Wojciech Szpankowski, Joachim Buhmann
Abstract
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 tight information-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.
BibTeX
@InProceedings{pmlr-v151-corinzia22a,
title = { Statistical and computational thresholds for the planted k-densest sub-hypergraph problem },
author = {Corinzia, Luca and Penna, Paolo and Szpankowski, Wojciech and Buhmann, Joachim},
booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics},
pages = {11615--11640},
year = {2022},
editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel},
volume = {151},
series = {Proceedings of Machine Learning Research},
month = {28--30 Mar},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v151/corinzia22a/corinzia22a.pdf},
url = {https://proceedings.mlr.press/v151/corinzia22a.html},
abstract = { 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 tight information-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. }
}