arXiv Machine Learning July 27, 2026 By Mario Sayde, Christopher Khater, Jihad Fahs, Ibrahim Abou-Faycal

Heavy-Tailed Principal Component Analysis

Read the original on arXiv Machine Learning →

arXiv: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.

Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.

efficiency

arXiv Machine Learning

Jul 7

PCA of probability measures: Sparse and Dense sampling regimes

arXiv:2602. 02190v2 Announce Type: replace-cross Abstract: A common approach to perform PCA on probability measures is to embed them into a Hilbert space where standard functional PCA techniques apply.

By Gachon Erell, J\'er\'emie Bigot, Elsa Cazelles

rag

arXiv Machine Learning

Jun 15

The Risk Shadow of Principal Component Analysis: When 99.9999% Variance Preservation Causes Catastrophic Decision Errors

arXiv:2606. 14533v1 Announce Type: new Abstract: Principal Component Analysis (PCA) preserves variance, not the information needed to detect rare catastrophic events.

By Hamidou Tembine

benchmarks

arXiv Machine Learning

Jun 2

Cellwise and Casewise Robust Covariance in High Dimensions

arXiv:2505. 19925v2 Announce Type: replace-cross Abstract: The sample covariance matrix is a cornerstone of multivariate statistics, but it is highly sensitive to outliers.

By Fabio Centofanti, Mia Hubert, Peter J. Rousseeuw

arXiv Machine Learning

Jun 8

Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization

arXiv:2604. 03146v2 Announce Type: replace-cross Abstract: We study high-dimensional convex empirical risk minimization (ERM) under general non-Gaussian data designs.

By Chiheb Yaakoubi, Cosme Louart, Malik Tiomoko, Zhenyu Liao

arXiv Machine Learning

Aug 11

Sparse corruption in low-rank matrix inference: the PCA benchmark

arXiv:2511. 11927v2 Announce Type: replace-cross Abstract: Principal Component Analysis (PCA) is a standard tool for extracting a low-rank signal from noisy observations.

By Urte Adomaityte, Gabriele Sicuro, Pierpaolo Vivo

benchmarks safety

arXiv Machine Learning

Jul 27

Data eccentricity, asymptotics of Gaussian RBF reproducing kernel Hilbert space, and kernel PCA

arXiv:2607. 21823v1 Announce Type: new Abstract: We show that, up to isotropic scaling, the Gaussian RBF reproducing kernel Hilbert space (RKHS) is asymptotically isometric to Euclidean space in the large bandwidth limit.

By Sergio A. Alvarez

rag

Related stories

PCA of probability measures: Sparse and Dense sampling regimes

The Risk Shadow of Principal Component Analysis: When 99.9999% Variance Preservation Causes Catastrophic Decision Errors

Cellwise and Casewise Robust Covariance in High Dimensions

Characterization of Gaussian Universality Breakdown in High-Dimensional Empirical Risk Minimization

Sparse corruption in low-rank matrix inference: the PCA benchmark

Data eccentricity, asymptotics of Gaussian RBF reproducing kernel Hilbert space, and kernel PCA