arXiv:2606. 24134v1 Announce Type: cross Abstract: Motivated by an application in machine learning optimization, this paper focuses on the challenges of sampling a matrix uniformly from the unit spectral norm ball.
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:2608. 12503v1 Announce Type: cross Abstract: We describe a simple rejection-sampling-based algorithm to perform length-squared sampling on an $n \times n$ positive-semidefinite (psd) matrix: that is, to sample a column with probability proportional to its squared $\ell_2$-norm.
The paper introduces two randomized approaches to accelerate spectral co‑clustering of word‑document matrices: one based on randomized SVD via random projection, and another combining partial SVD with element‑wise random sampling. Experiments on real and synthetic data show both methods cut runtime compared to full SVD, with the projection technique offering more consistent performance across varied sparsity levels, while the sampling method excels on denser matrices. The study highlights that the choice of approximation should align with the data’s structural properties.
arXiv:2607. 06644v1 Announce Type: cross Abstract: Determinantal point processes have recently emerged as a kernel-based alternative to standard independent sampling for constructing efficient minibatches, coresets, and other compact representations of large-scale datasets.
arXiv:2602. 05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion.
arXiv:2507.02248v2 Announce Type: replace-cross Abstract: In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank t...
arXiv:2507.19290v2 Announce Type: replace-cross Abstract: We study the problem of learning a structured approximation (low-rank, sparse, banded, etc.) to an unknown matrix $A$ given access to matrix-...
arXiv:2602. 20376v3 Announce Type: replace-cross Abstract: We study the problem of maximizing a complex-valued quadratic form over the $K^{\text{th}}$ roots of unity.
arXiv:2609.36271v1 Announce Type: new Abstract: Recent work has established that power-law spectral conditions on data enable tight convergence bounds for deterministic gradient descent, resolving th...
arXiv:2412. 16457v3 Announce Type: replace-cross Abstract: In this paper, we focus on the matching recovery problem between a pair of correlated Gaussian Wigner matrices with a latent vertex correspondence.
arXiv:2607. 11938v1 Announce Type: cross Abstract: This book is about the mathematical foundations of data science.
arXiv:2609.39173v1 Announce Type: new Abstract: In this paper, we consider asymptotic properties of the support vector machine (SVM) in high-dimension, low-sample-size (HDLSS) settings under a spiked...