arXiv Machine Learning
Sep 16
Near-Optimal Nonconvex Matrix Completion
arXiv:2609. 17048v1 Announce Type: cross Abstract: We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries.
Understanding Alternating Minimization for Matrix Completion
arXiv:1312. 0925v4 Announce Type: replace Abstract: Alternating Minimization is a widely used and empirically successful heuristic for matrix completion and related low-rank optimization problems.
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arXiv Machine Learning
Jul 21
Exploiting Low-Rank Objective Structure in Discrete Quadratic Optimization
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 Machine Learning
Aug 14
Fast Length-Squared Sampling for Positive-Semidefinite Matrices
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.
arXiv Machine Learning
Jun 19
Alternating Direction Method of Multipliers for Nonlinear Matrix Decompositions
arXiv:2512. 17473v3 Announce Type: replace-cross Abstract: We present an algorithm based on the alternating direction method of multipliers (ADMM) for solving nonlinear matrix decompositions (NMD).
arXiv Machine Learning
Jul 1
Direction-Magnitude Decomposition for Low-Rank Matrix Optimization: Faster Convergence and Saddle-to-saddle Dynamics
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 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 Computer Vision
Sep 15
Robust low-rank tensor completion via factorized weighted tensor schatten-p norm minimization
arXiv:2609.14307v1 Announce Type: new Abstract: Low-rank tensor factorization provides a flexible framework for completing multidimensional data from incomplete and corrupted observations. However, u...
arXiv Machine Learning
Aug 27
Maximum-Volume Nonnegative Matrix Factorization
arXiv:2602. 04795v3 Announce Type: replace Abstract: Nonnegative matrix factorization (NMF) is a popular data embedding technique.
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
Weighted Low-Rank Matrix Approximation: Acceleration and Applications
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 Statistics ML
Aug 25
Subzero matrix completion for sparse data analysis: large-scale learning of latent low-rank structure
arXiv:2608.21607v1 Announce Type: cross Abstract: We investigate when a sparse nonnegative matrix can be recovered from a real-valued matrix of much lower rank by zeroing out its negative elements. T...
arXiv Machine Learning
Aug 24
Query Efficient Structured Matrix Learning
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-...