Rigorous detection thresholds for spiked models

Determine rigorous signal detection thresholds for spiked models as a function of data type; specifically, establish precise detectability conditions for low-rank signals embedded in high-dimensional noise for spiked matrix and spiked tensor settings.

Background

The paper surveys state-of-the-art methods for signal detection in high-dimensional data and highlights limitations of principal component analysis in nearly continuous spectra. Within this context, it points out that theoretical understanding of detection limits in spiked models is incomplete.

The authors emphasize that while random matrix theory provides a mature framework for spiked matrices, extending rigorous detection thresholds to other data modalities—particularly tensors—remains challenging, partly due to connections with spin-glass phenomena and the comparatively less developed state of random tensor theory.