On Statistical-Computational Gaps in Graph Combinatorial Testing Problems
Read the original on arXiv Statistics ML →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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