arXiv Machine Learning
On Kernel Eigen-alignments of KRR: Reconstruction and Generalization
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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 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...
arXiv Machine Learning
Jul 28
Spectral-Aware Analytic Class-Incremental Learning for Long-Tailed Distributions
arXiv:2607. 22931v1 Announce Type: new Abstract: Analytic Continual Learning (ACL) offers a computationally efficient alternative to gradient-based approaches.
arXiv Machine Learning
Jun 10
Sample-efficient inductive matrix completion with noise and inexact side-information
arXiv:2605. 17189v2 Announce Type: replace-cross Abstract: Inductive matrix completion (IMC) is a variant of low-rank matrix completion that incorporates row and column side-information.
arXiv Machine Learning
Jul 24
Regularized Optimization on Grassmann Manifold: Theory, Algorithm and Applications
arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.
arXiv Machine Learning
1d ago
High-Dimensional Partial Least Squares: Spectral Analysis and Fundamental Limitations
The paper investigates Partial Least Squares (PLS) in high-dimensional settings, focusing on a model where two data matrices share a low-rank latent structure plus individual-specific components. By analyzing the singular vectors of the cross‑covariance matrix with random matrix theory, the authors derive asymptotic characterizations of how well the estimated latent directions align with the true ones. They show that the PLS variant based on Singular Value Decomposition (PLS‑SVD) outperforms separate principal component analysis in detecting the common latent subspace, while also identifying regimes where PLS‑SVD behaves counter‑intuitively or reaches fundamental limits.