Heavy-Tailed Principal Component Analysis

תקציר מקורי באנגליתarXiv:2603.11308v3 Announce Type: replace Abstract: Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise. While numerous robust PCA variants have been proposed, most either assume finite variance, rely on sparsity-driven decompositions, or address robustness through surrogate loss functions without a unified treatment of infinite-variance models. In this paper, we study PCA for high-dimensional data generated according to a superstatistical dependent model of the form $\mathbf{X} = A^{1/2}\mathbf{G}$, where $A$ is a positive random scalar and $\mathbf{G}$ is a Gaussian vector. This framework captures a wide cla