Distinguishability and Recovery for a Doubly Sparse Spiked Wigner Model
Read the original on arXiv Machine Learning →The paper investigates how to distinguish and recover a sparse rank‑one signal in a spiked Wigner model where both the signal and the noise are independently sparse. It introduces a leave‑one‑out quadratic thresholding method that identifies the signal support for sub‑Gaussian noise and bounded spikes, and shows that sign synchronization and spectral refinement can achieve exact or strong recovery for Rademacher spikes. The work also extends to sub‑Gaussian spike priors, provides an explicit trade‑off between signal sparsity, noise sparsity, and computational cost, and establishes recoverability conditions that do not rely on moment assumptions for continuous noise.
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