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• W2964025462 abstract "In this paper we study sharp thresholds for detecting sparse signals in $beta$-models for potentially sparse random graphs. The results demonstrate interesting interplay between graph sparsity, signal sparsity, and signal strength. In regimes of moderately dense signals, irrespective of graph sparsity, the detection thresholds mirror corresponding results in independent Gaussian sequence problems. For sparser signals, extreme graph sparsity implies that all tests are asymptotically powerless, irrespective of the signal strength. On the other hand, sharp detection thresholds are obtained, up to matching constants, on denser graphs. The phase transition mentioned above are sharp. As a crucial ingredient, we study a version of the Higher Criticism Test which is provably sharp up to optimal constants in the regime of sparse signals. The theoretical results are further verified by numerical simulations." @default.
• W2964025462 created "2019-07-30" @default.
• W2964025462 creator A5013076039 @default.
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• W2964025462 date "2018-06-01" @default.
• W2964025462 modified "2023-10-18" @default.
• W2964025462 title "Detection thresholds for the $beta$-model on sparse graphs" @default.
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• W2964025462 doi "https://doi.org/10.1214/17-aos1585" @default.
• W2964025462 hasPublicationYear "2018" @default.
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