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...
By Juno Kim, Hengyu Fu, Peter Bartlett, Jason D. Lee, Jingfeng Wu
arXiv:2608. 15351v1 Announce Type: new Abstract: Nominal LoRA rank is a design parameter; calibrated spectral evidence is a separate inferential quantity.
By Mohammed Ahnouch, Lotfi Elaachak
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...
By Qiang Sun
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...
By Xin Li, Jonathan Cohen, Rami Puzis
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.
By Zhenlin Yao, Wei Xiong
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