arXiv Machine Learning
Compact and Infinite-Order Error Analysis for Null-Space SVD Estimation
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arXiv Machine Learning
Aug 20
Inference and Uncertainty Quantification for Streaming $r$-PCA
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.
arXiv Machine Learning
Jun 16
Stochastic trace estimation with tensor train random vectors
arXiv:2606. 15679v1 Announce Type: cross Abstract: Stochastic trace estimation is a standard tool for approximating the trace of a large-scale matrix available only through matrix-vector products.
arXiv Machine Learning
Aug 18
Spectral Rank Certification for Foundation Model Adapters
arXiv:2608. 15351v1 Announce Type: new Abstract: Nominal LoRA rank is a design parameter; calibrated spectral evidence is a separate inferential quantity.
arXiv Machine Learning
Jul 31
Tight Sample Complexity for Low-Rank Adaptation: Matching Bounds and Rank Selection
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 Machine Learning
Sep 10
Diagonal Attenuation: A Finite-Sample Correction for PCA
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 Statistics ML
Sep 10
A Subsampled Davis-Kahan Bound for Large-Scale Eigenspace Estimation
arXiv:2609.09211v1 Announce Type: new Abstract: The Davis-Kahan theorem is a fundamental tool in spectral analysis, providing quantitative control over the distance between the eigenspaces of a symme...