2013
DOI: 10.3150/12-bej470
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Detection of a sparse submatrix of a high-dimensional noisy matrix

Abstract: We observe a $N\times M$ matrix $Y_{ij}=s_{ij}+\xi_{ij}$ with $\xi_{ij}\sim {\mathcal {N}}(0,1)$ i.i.d. in $i,j$, and $s_{ij}\in \mathbb {R}$. We test the null hypothesis $s_{ij}=0$ for all $i,j$ against the alternative that there exists some submatrix of size $n\times m$ with significant elements in the sense that $s_{ij}\ge a>0$. We propose a test procedure and compute the asymptotical detection boundary $a$ so that the maximal testing risk tends to 0 as $M\to\infty$, $N\to\infty$, $p=n/N\to0$, $q=m/M\to0$. … Show more

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Cited by 96 publications
(167 citation statements)
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“…. , a stopping time T which indicates the time when we stop sampling, and the estimator S. In what follows we consider always the definition of the two last quantities given by (5) and (6). The queries Q t will be defined separately for each special case.…”
Section: General Analysis Of Algorithmmentioning
confidence: 99%
See 2 more Smart Citations
“…. , a stopping time T which indicates the time when we stop sampling, and the estimator S. In what follows we consider always the definition of the two last quantities given by (5) and (6). The queries Q t will be defined separately for each special case.…”
Section: General Analysis Of Algorithmmentioning
confidence: 99%
“…, n} : e i ∩ e T ′ = ∅ . The stopping time T and estimator S are defined as usual in (5) and (6). Note that this is an instance of the general procedure described in the setting of Proposition 3 with K = 1 and l 1 = 1.…”
Section: S-starsmentioning
confidence: 99%
See 1 more Smart Citation
“…, n}. CDEP as a risk measure has been considered in the literature for detecting abnormal clusters in a network (see e.g., [4,10]). It also provides an upper bound on the Bayesian risk measure.…”
Section: Detection Procedures Based On Generalized Likelihood Ratio Testmentioning
confidence: 99%
“…This corresponds to a symmetric version of the submatrix localization problem studied in [37,30,10,9,31,12,11]. 1 When µ > 0, the entries of A with row and column indices in C * have positive mean µ except those on the diagonal, while the rest of the entries have zero mean.…”
Section: Introductionmentioning
confidence: 99%