A1143
Title: Signal detection from spiked noise via asymmetrization
Authors: Zhigang Bao - The University of Hong Kong (Hong Kong) [presenting]
Abstract: The signal-plus-noise model is a fundamental framework in signal detection, where a low-rank signal is corrupted by noise. In the high-dimensional setting, one often uses the leading singular values and corresponding singular vectors of the data matrix to conduct statistical inference on the signal component. Specifically, when the noise consists of i.i.d. random entries, the singular values of the signal component can be estimated from those of the data matrix, provided the signal is sufficiently strong. However, when the noise entries are heteroscedastic or correlated, this standard approach may fail. In particular, a challenging scenario that arises with heteroscedastic noise is considered: When the noise itself can create spiked singular values. This raises the recurring question of how to distinguish the signal from the spikes in the noise. To address this, the eigenvalues of an asymmetrized model are studied when two samples are available. It is demonstrated that by examining the leading eigenvalues (in magnitude) of the asymmetrized model, one can reliably detect the signal. This approach is effective even in the heavy-tailed regime, where the singular value method fails.
