Spectral Phase Transition and Optimal PCA in Block-Structured Spiked models

arXiv:2403.03695v1 Announce Type: cross
Abstract: We discuss the inhomogeneous spiked Wigner model, a theoretical framework recently introduced to study structured noise in various learning scenarios, through the prism of random matrix theory, with a specific focus on its spectral properties. Our primary objective is to find an optimal spectral method and to extend the celebrated \cite{BBP} (BBP) phase transition criterion -- well-known in the homogeneous case -- to our inhomogeneous, block-structured, Wigner model. We provide a thorough rigorous analysis of …

abstract arxiv block cond-mat.dis-nn cs.lg discuss focus framework math.pr math.st matrix noise random stat.ml stat.th study theory through transition type