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:2609.39440v1 Announce Type: new Abstract: We compare the instance-wise, finite-sample risks of monotone spectral filters for linear regression, a broad class of estimators including principal c...
arXiv:2608. 15351v1 Announce Type: new Abstract: Nominal LoRA rank is a design parameter; calibrated spectral evidence is a separate inferential quantity.
arXiv:2609.05796v1 Announce Type: cross Abstract: Principal component analysis (PCA) can rotate away from its population target when a covariance matrix is estimated from limited data. We introduce d...
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...
The paper studies Online Kernel Supervised Principal Component Analysis (OKSPCA), which uses random features and an Adam-style orthonormal basis update to optimize a supervised spectral objective. It shows that accurate optimization of this objective does not guarantee accurate population subspace recovery or improved predictive performance, and it provides theoretical results on consistency, concentration, and perturbation of the estimator. Empirical experiments on six benchmarks reveal that replacing the tracker with the exact empirical target does not significantly change regression deficits, while classification-rank models capture most of the terminal objective energy but can exhibit substantial geometric deviation; sample-size studies further separate empirical accuracy from population recovery. The diagnostics also compare computational trade-offs, indicating that exact on-request computation can be faster in classification settings, whereas Adam saves time relative to full thin‑SVD in some dense regression requests, despite persistent geometric error.
arXiv:2606. 14533v1 Announce Type: new Abstract: Principal Component Analysis (PCA) preserves variance, not the information needed to detect rare catastrophic events.
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...
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:2607. 27680v1 Announce Type: new Abstract: Low-Rank Adaptation (LoRA) has become the standard mechanism for fine-tuning large pretrained models, yet its statistical properties remain only partially understood.
arXiv:2609.38901v1 Announce Type: new Abstract: Representer explanations rank the training landmarks that most influence a self-supervised representation. At scale, this ranking rests on up to four s...
arXiv:2605.15240v2 Announce Type: replace-cross Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
The paper tackles two key gaps in streaming PCA using Oja's algorithm: it establishes sharp operator‑norm convergence for general‑rank subspaces under sub‑Gaussian data, and it provides distributional inference for the resulting subspace estimator. The authors remove non‑vanishing remainder terms from existing analyses, achieving rates that match minimax bounds in both dense‑tail and sparse‑tail regimes. They further develop a linearization of Oja’s iterates, enabling high‑dimensional Gaussian approximations and an online multiplier bootstrap for practical inference.