Detection of Signal in the Spiked Rectangular Models

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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-P\'ech\'e (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.
Publisher
ICML committee
Issue Date
2021-07-22
Language
English
Citation

Thirty-eighth International Conference on Machine Learning (ICML)

ISSN
2640-3498
URI
http://hdl.handle.net/10203/286835
Appears in Collection
EE-Conference Papers(학술회의논문)MA-Conference Papers(학술회의논문)
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