The paper investigates high‑dimensional graph combinatorial hypothesis testing where a signal resides on the edges of an unknown subgraph. For Gaussian observations, it derives sharp statistical and computational thresholds for detecting the signal across various graph alternatives, using second‑moment bounds of likelihood ratios and low‑degree methods. The authors also establish a transfer principle linking exponential family models, identify new statistical‑computational gaps for structures like multiple planted cliques and hypercliques, and provide matching upper bounds under local regularity, thereby revealing universal threshold scales and connecting Gaussian and Erdős–Rényi settings.
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arXiv:2508. 02158v2 Announce Type: replace-cross Abstract: Detection of planted subgraphs in Erd\"os-R\'enyi random graphs has been extensively studied, leading to a rich body of results characterizing both statistical and computational thresholds.
Cluster labels are often used twice: first to discover groups, and then to test whether the discovered groups differ. This double use of the data makes ordinary two-sample $p$-values anti-conservative...
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arXiv:2511. 17240v3 Announce Type: replace-cross Abstract: We study the problem of learning an unknown graph via group queries on node subsets, where each query reports whether at least one edge is present among the queried nodes.
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