Weak Detection in the Spiked Wigner Model

Chung, Hye Won; Lee, Ji Oon

doi:10.1109/tit.2022.3185232

Cited by 6 publications

(33 citation statements)

References 34 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…For the subcritical case where it is impossible to reliably detect the signal by the improved PCA, we propose algorithms for weak detection, based on the central limit theorem (CLT) of the LSS, Theorems 5.2, 5.3, 5.5, and 5.6, analogous to the ones introduced in [22]. More precisely, assuming the SNRs are uniform i.e., Λ = λI, we propose an algorithm for a hypothesis test between…”

Section: Main Contributionsmentioning

confidence: 99%

“…Our test in Algorithm 2 verifies the claim since the error of the proposed test is an increasing function of (k 2 − k 1 ) as in Theorem 4.2. As in [22], the proposed tests are universal, and the various quantities in it can be estimated from the observed data. The test can further be improved by applying the same entrywise transformation we used for the PCA (Algorithm 3) if the data matrix is of additive type (spiked Wigner matrix or rectangular matrix with spiked mean), and it also can be adapted to the rank detection problem where we need to estimate the rank k of the signal without knowing the candidates k 1 and k 2 a priori (Algorithm 4).…”

Section: Main Contributionsmentioning

confidence: 99%

“…Though optimal, the LR test is not efficient, and it is desirable to construct a test that does not depend on information about the prior, which is typically not known in many practical applications. In [22], an optimal and universal test for spiked Wigner matrices was proposed, which is based on the linear spectral statistics (LSS) of the data matrix, a linear functional defined as…”

Section: Introductionmentioning

confidence: 99%

“…In this improved PCA, the threshold is lowered by a certain factor that depends on the Fisher information of the noise distribution. Below this threshold, the LSS-based test proposed in [22] for spiked Wigner matrices can also be improved by applying the entrywise transformation for the improved PCA. It is not known whether the reliable detection is impossible below the threshold except for the case of the spiked Wigner matrix with Rademacher prior [21].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Detection problems in the spiked matrix models

Jung¹,

Chung²,

Lee³

2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

Section: Main Contributionsmentioning

confidence: 99%

Section: Main Contributionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Detection problems in the spiked matrix models

Jung¹,

Chung²,

Lee³

2023

Preprint

View full text Add to dashboard Cite

show abstract

“…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

View full text Add to dashboard Cite

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.

show abstract

Phase transition for the generalized two-community stochastic block model

Lee,

Lee

2023

J. Appl. Probab.

View full text Add to dashboard Cite

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.

show abstract

Weak Detection in the Spiked Wigner Model

Cited by 6 publications

References 34 publications

Detection problems in the spiked matrix models

Detection problems in the spiked matrix models

Phase Transition in the Generalized Stochastic Block Model

Phase transition for the generalized two-community stochastic block model

Contact Info

Product

Resources

About