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Detection of Signal in the Spiked Rectangular Models
Ji Hyung Jung · Hye Won Chung · Ji Oon Lee

Wed Jul 21 09:00 PM -- 11:00 PM (PDT) @ Virtual

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.

Author Information

Ji Hyung Jung (KAIST)
Hye Won Chung (KAIST)
Ji Oon Lee (KAIST)

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