Tensor Completion

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Period ending 2026-09-21

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26 papers

Latest in Tensor Completion

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Near-Optimal Nonconvex Matrix Completion
Sep 15, 2026Jian-Feng Cai, Xiliang Lu, Juntao YouTensor Completion Convex Optimization
Coupled Tensor-Tensor Completion Method with Applications in Drug Repurposing
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Robust Low-Tubal-Rank Tensor Completion under Cross-Concentrated Sampling
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Graph-Regularized Low-Rank Matrix Completion by Variable Projection
Jul 10, 2026Benoît Loucheur, P. -A. Absil, Michel JournéeTensor Completion Low-Rank Factorization
CollabEval: Statistically Efficient Collaborative Model Evaluation via Matrix Completion
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Dual-Attention Convolution Experts for Sparse Tensor Completion
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Low-Rank Tensor Completion Based on Fractional Regularization with Ky Fan p-k Norm
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Robust Neural Tucker Factorization with Bias Correction and Adaptive Initialization
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Latent Structural Categorical Matrix Completion with Application to Quasispecies Analysis
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Low-rank Distributional Matrix Completion
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Spectra-Guided Neural Tucker Factorization
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Open Problem: Separating Geometric and Algorithmic Compression via Cayley-Table Completion
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Group-Aware Matrix Estimation and Latent Subspace Recovery
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Sample-efficient inductive matrix completion with noise and inexact side-information
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Low Rank Tensor Completion via Adaptive ADMM
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Active multiple matrix completion with adaptive confidence sets
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Inductive Convolution Nuclear Norm Minimization for Tensor Completion with Arbitrary Sampling
Apr 18, 2026Wei Li, Yuyang Li, Kaile Du +2Tensor Completion Tensor
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Dec 1, 2023Wanteng Ma, Lilun Du, Dong Xia +1Tensor Completion False Discovery Rate

Sep 15, 2026 · math.NAJ/K move · Enter open · S save

Near-Optimal Nonconvex Matrix Completion

Jian-Feng Cai, Xiliang Lu, Juntao You

Department of Mathematics, Hong Kong University of Science and Technology. · School of Mathematics and Statistics, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China. · School of Artificial Intelligence, Hubei Center for Applied Mathematics, and Hubei Key Laboratory of Computational Science, Wuhan University, Wuhan 430072, China.

We study nonconvex methods for matrix completion, the problem of recovering a low-rank matrix from a subset of its entries. Convex methods achieve sample complexity linear in the matrix dimension and the rank, up to logarithmic factors, whereas global guarantees for commonly used nonconvex methods require a higher polynomial dependence on the rank. We close this gap by analyzing Riemannian gradient descent (RGD) and Riemannian Gauss--Newton (RGN) methods. For an

n\times n

matrix of rank

r

with incoherence parameter

μ

and condition number

κ

, the two methods achieve exact recovery with high probability from

O(μnr\log n\log(nκ))

and

O(μnr\log n\log(2μrκ))

observations, respectively. The methods use a multiscale residual initialization, while the analysis simultaneously controls the spectral error and incoherence. The resulting RGD iterates converge linearly, whereas RGN eventually converges Q-quadratically.

Tensor Completion Convex Optimization Sample Complexity

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