arXiv Machine Learning
Diagonal Attenuation: A Finite-Sample Correction for PCA
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Heavy-Tailed Principal Component Analysis
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.
arXiv Machine Learning
Sep 1
Compact and Infinite-Order Error Analysis for Null-Space SVD Estimation
arXiv:2608.30374v1 Announce Type: cross Abstract: We study null-space estimation from a noisy matrix. For a simple left null space, we first derive an exact compact expression for the error of the sm...
arXiv Machine Learning
Jul 21
De-floored Principal Component Regression: When Rank Selection Alone Is Insufficient for Prediction
arXiv:2607. 16638v1 Announce Type: cross Abstract: Principal component regression (PCR) regularizes high-dimensional prediction by choosing a spectral cutoff, but rank selection cannot correct systematic inflation of the retained empirical eigenvalues.
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.
arXiv Machine Learning
Jun 2
Global Convergence of Adaptive Sensing for Principal Eigenvector Estimation
arXiv:2505. 10882v2 Announce Type: replace Abstract: Principal component analysis classically requires full $d$-dimensional samples, yet in various applications hardware limits acquisition to a few scalar measurements per sample.
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.