Weak Detection of Signal in the Spiked Wigner Model

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We consider the problem of detecting the presence of the signal in a rank-one signal-plus-noise data matrix. In case the signal-to-noise ratio is under the threshold below which a reliable detection is impossible, we propose a hypothesis test based on the linear spectral statistics of the data matrix. When the noise is Gaussian, the error of the proposed test is optimal as it matches the error of the likelihood ratio test that minimizes the sum of the Type-I and Type-II errors. The test is data-driven and does not depend on the distribution of the signal or the noise. If the density of the noise is known, it can be further improved by an entrywise transformation to lower the error of the test.
Publisher
ICML committee
Issue Date
2019-06-11
Language
English
Citation

Thirty-sixth International Conference on Machine Learning (ICML)

ISSN
2640-3498
URI
http://hdl.handle.net/10203/269398
Appears in Collection
EE-Conference Papers(학술회의논문)MA-Conference Papers(학술회의논문)
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