Detection of Signal in the Spiked Rectangular Models

Ji Hyung Jung, Hye Won Chung, Ji Oon Lee
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:5158-5167, 2021.

Abstract

We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik–Ben Arous–Péché (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-jung21a, title = {Detection of Signal in the Spiked Rectangular Models}, author = {Jung, Ji Hyung and Chung, Hye Won and Lee, Ji Oon}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {5158--5167}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/jung21a/jung21a.pdf}, url = {https://proceedings.mlr.press/v139/jung21a.html}, abstract = {We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik–Ben Arous–Péché (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.} }
Endnote
%0 Conference Paper %T Detection of Signal in the Spiked Rectangular Models %A Ji Hyung Jung %A Hye Won Chung %A Ji Oon Lee %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-jung21a %I PMLR %P 5158--5167 %U https://proceedings.mlr.press/v139/jung21a.html %V 139 %X We consider the problem of detecting signals in the rank-one signal-plus-noise data matrix models that generalize the spiked Wishart matrices. We show that the principal component analysis can be improved by pre-transforming the matrix entries if the noise is non-Gaussian. As an intermediate step, we prove a sharp phase transition of the largest eigenvalues of spiked rectangular matrices, which extends the Baik–Ben Arous–Péché (BBP) transition. We also propose a hypothesis test to detect the presence of signal with low computational complexity, based on the linear spectral statistics, which minimizes the sum of the Type-I and Type-II errors when the noise is Gaussian.
APA
Jung, J.H., Chung, H.W. & Lee, J.O.. (2021). Detection of Signal in the Spiked Rectangular Models. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:5158-5167 Available from https://proceedings.mlr.press/v139/jung21a.html.

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