arXiv:2607. 09546v1 Announce Type: new Abstract: We address the low-rank matrix completion problem by incorporating graph regularization into the existing Riemannian Trust-Region Matrix Completion (RTRMC) framework.
arXiv:2607. 21039v1 Announce Type: new Abstract: Spectral methods are among the most widely used techniques for community detection, clustering, and graph learning.
arXiv:2606. 04176v1 Announce Type: new Abstract: We study a distributional generalization of the matrix completion problem in which each entry of the target matrix is a probability distribution rather than a scalar.
arXiv:2606. 01216v1 Announce Type: new Abstract: The elementwise Hadamard product of two low-rank matrices provides a parameter-efficient model for data with multiplicative structure, but its modeling is challenging due to the presence of additional symmetries under coupled row/column scalings between the two factors.
arXiv:2607. 22436v1 Announce Type: cross Abstract: This work addresses the generation of theoretical correlation matrices with prescribed sparsity patterns associated to graph structures.
arXiv:2607. 11938v1 Announce Type: cross Abstract: This book is about the mathematical foundations of data science.
arXiv:2606. 31390v1 Announce Type: cross Abstract: Low-rank matrix optimization is often carried out via the Burer-Monteiro (BM) formulation, but choosing the factorization rank $r$ is delicate and can substantially slow optimization.
arXiv:2503. 24075v4 Announce Type: replace-cross Abstract: Low-rank optimization problems with sparse simplex constraints involve variables that must satisfy nonnegativity, sparsity, and sum-to-1 conditions, making their optimization particularly challenging due to the interplay between low-rank structures and constraints.
arXiv:2510. 01878v2 Announce Type: replace Abstract: Low-rank gradient optimization for large language models is currently divided into two categories: structured methods that rigorously identify subspaces, and randomized approaches employed primarily for computational efficiency.
arXiv:2312. 00305v3 Announce Type: replace-cross Abstract: Many important tasks of large-scale recommender systems can be naturally cast as testing multiple linear forms for noisy matrix completion.
arXiv:2109. 11057v2 Announce Type: replace-cross Abstract: Weighted low-rank matrix approximation (WLRMA) generalizes classical low-rank approximation and matrix completion by allowing arbitrary elementwise weights.
arXiv:2606. 12120v1 Announce Type: new Abstract: Low-rank optimal transport (OT) mitigates the quadratic scaling of classical solvers, yet existing approaches rely heavily on first-order mirror-descent updates that require careful hyperparameter tuning and ignore the optimization landscape's curvature.
arXiv:2606. 00413v1 Announce Type: cross Abstract: Sufficient dimension reduction (SDR) makes high-dimensional regression tractable by projecting the covariates onto a low-dimensional subspace that preserves the conditional mean of the response.