2018
DOI: 10.48550/arxiv.1811.05124
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Fundamental Limits of Exact Support Recovery in High Dimensions

Abstract: We study the support recovery problem for a high-dimensional signal observed with additive noise. With suitable parametrization of the signal sparsity and magnitude of its non-zero components, we characterize a phase-transition phenomenon akin to the signal detection problem studied by Ingster in 1998. Specifically, if the signal magnitude is above the so-called strong classification boundary, we show that several classes of well-known procedures achieve asymptotically perfect support recovery as the dimension… Show more

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Cited by 2 publications
(30 citation statements)
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“…In terms of the more stringent exact support recovery probability (2.5), several well-known FWER-controlling procedures -including Bonferroni's procedure -have been shown to be optimal in the additive error model under one-sided alternatives [14]. Optimality results were also obtained for a specific procedure under the expected Hamming loss (E[ S△S]) in [7], where the asymptotic analyses focused exclusively on the two-sided alternatives.…”
Section: Discussionmentioning
confidence: 99%
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“…In terms of the more stringent exact support recovery probability (2.5), several well-known FWER-controlling procedures -including Bonferroni's procedure -have been shown to be optimal in the additive error model under one-sided alternatives [14]. Optimality results were also obtained for a specific procedure under the expected Hamming loss (E[ S△S]) in [7], where the asymptotic analyses focused exclusively on the two-sided alternatives.…”
Section: Discussionmentioning
confidence: 99%
“…Therefore, a theory for the chi-square model (1.1) naturally lends itself to the study of two-sided alternatives in the Gaussian additive error model (1.3). In comparing such results with existing theory on one-sided alternatives [2,14], we will be able to quantify if, and how much of a price has to be paid for the additional uncertainty when we have no prior knowledge on the direction of the signals.…”
Section: One-sided Vs Two-sided Alternatives In Additive Error Modelsmentioning
confidence: 99%
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