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: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: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: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: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:2606. 14533v1 Announce Type: new Abstract: Principal Component Analysis (PCA) preserves variance, not the information needed to detect rare catastrophic events.
arXiv:2607. 01895v1 Announce Type: new Abstract: We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix.
arXiv:2304.06522v3 Announce Type: replace-cross Abstract: Signal extraction is difficult when the number of variables $N$ is much larger than the number of observations $M$. We address this problem u...
arXiv:2608. 13365v1 Announce Type: new Abstract: Rotation-based post-training quantisation commonly applies an orthogonal transform across an entire attention head to reduce outlier-induced error.
arXiv:2608. 15313v1 Announce Type: cross Abstract: In this paper, we propose SHOPCA (Shape Operator-based Principal Component Analysis), a novel method for unsupervised metric learning and dimensionality reduction that incorporates differential geometric information into the covariance structure of classical PCA.
arXiv:2603.19657v2 Announce Type: replace-cross Abstract: We study model-order selection and component-mean estimation for multidimensional Gaussian mixture models with a known common covariance matr...
The paper extends prior work on volume sampling by providing a Loewner envelope for the centered coefficient covariance in least‑squares regression with a fixed pool of features and responses. It characterizes when this envelope is tight, linking tightness to strict spectral properties of residuals, and introduces a residual‑augmented change of measure to derive a one‑sided slack bound. The results also offer geometric insights at the boundary and demonstrate non‑vacuous certificates through frozen‑feature examples, focusing on conditional centered, full‑Gram‑whitened covariance rather than population generalization.