Guaranteed Nonconvex Low-Rank Tensor Estimation via Scaled Gradient Descent

arXiv:2501.01696 · stat.ML, cs.IT, cs.LG, math.IT · Submitted 2025-01-03 · Read on arXiv

stat.ML, cs.IT, cs.LG, math.IT

Submitted: 2025-01-03

Updated: 2026-02-14

Comments: This paper has been accepted for publication in the Journal of Machine Learning Research

Journal ref: Journal of Machine Learning Research 27(9):1-90, 2026

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

Alignment — 16× in this paper · explained in 1 episode
Matrix Completion — 10× in this paper · explained in 3 episodes
Theoretical Guarantees — 7× in this paper · explained in 2 episodes
Accuracy — 5× in this paper · explained in 1 episode
Clustering — 4× in this paper · explained in 2 episodes
Objective Function — 4× in this paper · explained in 2 episodes
Tucker Decomposition — 4× in this paper · explained in 2 episodes
Loss Function — 3× in this paper · explained in 2 episodes
Regularization — 3× in this paper · explained in 3 episodes
Trace — 3× in this paper · explained in 2 episodes
Reconstruction Error — 2× in this paper · explained in 2 episodes
Sample Complexity — 2× in this paper · explained in 15 episodes
Sparsity — 2× in this paper · explained in 4 episodes
Alternating Minimization — 1× in this paper · explained in 1 episode
Ambient Dimension — 1× in this paper · explained in 1 episode
Benchmark — 1× in this paper · explained in 2 episodes
Discrete Cosine Transform — 1× in this paper
Discrete Fourier Transform — 1× in this paper
Peak Signal-to-Noise Ratio — 1× in this paper
ScaledGD on the Background Models Challenge — 1× in this paper
Self-Supervised Learning — 1× in this paper · explained in 7 episodes

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