Weak Detection of Signal in the Spiked Wigner Model
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Proceedings of the 36th International Conference on Machine Learning, PMLR 97:12331241, 2019.
Abstract
We consider the problem of detecting the presence of the signal in a rankone signalplusnoise data matrix. In case the signaltonoise 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 TypeI and TypeII errors. The test is datadriven 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.
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