Weak Detection in the Spiked Wigner Model with General Rank

Jung, Ji Hyung; Chung, Hye Won; Lee, Ji Oon

doi:10.48550/arxiv.2001.05676

Cited by 4 publications

(5 citation statements)

References 15 publications

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“…The optimal error for the weak detection, achieved by the LR test, coincides with the limiting error in (4.15) when the noise is Gaussian and the SNR ω is sufficiently small; see [33]. Thus, our proposed test is optimal in this case.…”

Section: Signal Detection In Rank-k Spiked Modelssupporting

confidence: 69%

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Detection problems in the spiked matrix models

Jung¹,

Chung²,

Lee³

2023

Preprint

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We study the statistical decision process of detecting the low-rank signal from various signal-plusnoise type data matrices, known as the spiked random matrix models. We first show that the principal component analysis can be improved by entrywise pre-transforming the data matrix if the noise is non-Gaussian, generalizing the known results for the spiked random matrix models with rank-1 signals. As an intermediate step, we find out sharp phase transition thresholds for the extreme eigenvalues of spiked random matrices, which generalize the Baik-Ben Arous-Péché (BBP) transition. We also prove the central limit theorem for the linear spectral statistics for the spiked random matrices and propose a hypothesis test based on it, which does not depend on the distribution of the signal or the noise. When the noise is non-Gaussian noise, the test can be improved with an entrywise transformation to the data matrix with additive noise. We also introduce an algorithm that estimates the rank of the signal when it is not known a priori.

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Section: Signal Detection In Rank-k Spiked Modelssupporting

confidence: 69%

“…By performing the same calculations as we will do in this section, we can obtain optimal functions for the other models, so we omit the details. (Refer to [22,33,34]…”

Section: B52 Multiplicative Modelmentioning

confidence: 99%

Detection problems in the spiked matrix models

Jung¹,

Chung²,

Lee³

2023

Preprint

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show abstract

“…Reliable detection is impossible below a certain threshold [25], and it is only possible to consider a weak detection, which is a hypothesis testing between the null model (without spike) and the alternative (with spike). We refer to [12,14,21] for more detail about weak detection.…”

Section: Related Workmentioning

confidence: 99%

Phase transition for the generalized two-community stochastic block model

Lee,

Lee

2023

J. Appl. Probab.

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We study the problem of detecting the community structure from the generalized stochastic block model with two communities (G2-SBM). Based on analysis of the Stieljtes transform of the empirical spectral distribution, we prove a Baik–Ben Arous–Péché (BBP)-type transition for the largest eigenvalue of the G2-SBM. For specific models, such as a hidden community model and an unbalanced stochastic block model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition.

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“…Reliable detection is impossible below a certain threshold [21], and it is only possible to consider a weak detection, which is a hypothesis testing between the null model (without spike) and the alternative (with spike). For more detail about the weak detection, we refer to [12,10,19].…”

Section: Related Workmentioning

confidence: 99%

Phase Transition in the Generalized Stochastic Block Model

Lee¹,

Lee²

2022

Preprint

Self Cite

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We study the problem of detecting the community structure from the generalized stochastic block model (GSBM). Based on the analysis of the Stieljtes transform of the empirical spectral distribution, we prove a BBP-type transition for the largest eigenvalue of the GSBM. For specific models such as a hidden community model and an unbalanced stochastic model, we provide precise formulas for the two largest eigenvalues, establishing the gap in the BBP-type transition.

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Weak Detection in the Spiked Wigner Model with General Rank

Cited by 4 publications

References 15 publications

Detection problems in the spiked matrix models

Detection problems in the spiked matrix models

Phase transition for the generalized two-community stochastic block model

Phase Transition in the Generalized Stochastic Block Model

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