Weak Detection of Signal in the Spiked Wigner Model

Hye Won Chung, Ji Oon Lee
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:1233-1241, 2019.

Abstract

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-chung19a, title = {Weak Detection of Signal in the Spiked Wigner Model}, author = {Chung, Hye Won and Lee, Ji Oon}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {1233--1241}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/chung19a/chung19a.pdf}, url = {https://proceedings.mlr.press/v97/chung19a.html}, abstract = {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.} }
Endnote
%0 Conference Paper %T Weak Detection of Signal in the Spiked Wigner Model %A Hye Won Chung %A Ji Oon Lee %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-chung19a %I PMLR %P 1233--1241 %U https://proceedings.mlr.press/v97/chung19a.html %V 97 %X 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.
APA
Chung, H.W. & Lee, J.O.. (2019). Weak Detection of Signal in the Spiked Wigner Model. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:1233-1241 Available from https://proceedings.mlr.press/v97/chung19a.html.

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