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.
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.
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arXiv Machine Learning
Aug 11
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.
arXiv Statistics ML
Sep 22
Tensor Completion using Subspace Information
Tensor Completion using Subspace Information (TCSI) is an algorithm that leverages side information by estimating a subspace and reformulating tensor completion as a matrix regression problem. Theoretical analysis shows that accurate subspace information reduces sample complexity to nearly linear in the uncoupled ambient dimensions and relaxes signal-to-noise ratio requirements compared to existing guarantees. Numerical simulations and an application to reconstructing global Total Electron Content (TEC) maps demonstrate lower reconstruction errors than competing methods.
arXiv Machine Learning
Jun 9
Wedge Sampling: Efficient Tensor Completion with Nearly-Linear Sample Complexity
arXiv:2602. 05869v2 Announce Type: replace-cross Abstract: We introduce Wedge Sampling, a new non-adaptive sampling scheme for low-rank tensor completion.
arXiv Machine Learning
Jun 26
Fast algorithms for learning a Gaussian under halfspace truncation with optimal sample complexity
arXiv:2606. 27298v1 Announce Type: cross Abstract: We study the fundamental problem of learning a high-dimensional Gaussian truncated to an unknown halfspace.
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
Sep 22
On Kernel Eigen-alignments of KRR: Reconstruction and Generalization
arXiv:2605.15240v2 Announce Type: replace-cross Abstract: This paper investigates the critical role of eigenalignments between the kernel matrix and learning targets in achieving robust generalizatio...
arXiv Machine Learning
Jul 10
The Regularization Parameter: Sparse Precision Matrix Estimation
arXiv:2607. 07735v1 Announce Type: cross Abstract: Sparse precision matrix estimation provides an interpretable and computationally efficient framework for modeling conditional dependencies in high-dimensional, low-sample-size data.
arXiv Machine Learning
Jul 9
Fast Rates for Semi-Supervised Learning via Data-Augmentation Graph Regularization
arXiv:2607. 07513v1 Announce Type: new Abstract: Self-supervised learning matches supervised accuracy from a fraction of the labels, but the labeled-sample efficiency behind this has lacked a theoretical explanation.
arXiv Machine Learning
Jul 23
Stability of Low-Rank Implicit Regularization in Perturbed Deep Matrix Factorization
arXiv:2605. 28613v2 Announce Type: replace-cross Abstract: This paper studies the stability of low-rank implicit regularization in deep matrix factorization, a tractable model for understanding how gradient-based training can favor low-complexity structure.
arXiv Machine Learning
Jul 14
Demixing Sparse Signals from Nonlinear Observations using Generalized Non-convex Regularization
arXiv:2607. 10618v1 Announce Type: cross Abstract: We consider the recovery of a pair of sparse vectors from a limited number of nonlinear observations of their superposition: $y_i=g(\inner{\ba_i}{\bPhi\bw^\ast+\bPsi\bz^\ast})+e_i$, $i=1,\dots,m$, with $m\ll n$, incoherent orthonormal bases $\bPhi,\bPsi$, a scalar link $g$, and noise $e_i$ that may be heavy-tailed or contaminated.
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.