mlsanityData to 7 Oct 2026

An Optimal Statistical and Computational Framework for Generalized Tensor Estimation

arXiv 2002.11255 ↗First posted 26 Feb 2020math.ST cs.LG stat.MEcited by 39

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Abstract (arXiv)

This paper describes a flexible framework for generalized low-rank tensor estimation problems that includes many important instances arising from applications in computational imaging, genomics, and network analysis. The proposed estimator consists of finding a low-rank tensor fit to the data under generalized parametric models. To overcome the difficulty of non-convexity in these problems, we introduce a unified approach of projected gradient descent that adapts to the underlying low-rank structure. Under mild conditions on the loss function, we establish both an upper bound on statistical error and the linear rate of computational convergence through a general deterministic analysis. Then we further consider a suite of generalized tensor estimation problems, including sub-Gaussian tensor PCA, tensor regression, and Poisson and binomial tensor PCA. We prove that the proposed algorithm achieves the minimax optimal rate of convergence in estimation error. Finally, we demonstrate the superiority of the proposed framework via extensive experiments on both simulated and real data.

Key facts. Cited by 39 papers in the map (data through 7 Oct 2026). First posted on arXiv 26 Feb 2020.

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Citing papers per year: 2021: 8; 2022: 6; 2023: 6; 2024: 6; 2025: 7; 2026: 6.

39 papers.

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  1. 2021Scaling and Scalability: Provable Nonconvex Low-Rank Tensor Estimation from Incomplete Measurementscited by 28
  2. 2021Provable Tensor-Train Format Tensor Completion by Riemannian Optimizationcited by 17
  3. 2022Tensor-on-Tensor Regression: Riemannian Optimization, Over-parameterization, Statistical-computational Gap, and Their Interplaycited by 15
  4. 2021Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergencecited by 13
  5. 2021Latent Space Model for Higher-order Networks and Generalized Tensor Decompositioncited by 13
  6. 2022Fast and Provable Tensor Robust Principal Component Analysis via Scaled Gradient Descentcited by 11
  7. 2024On the Complexity of First-Order Methods in Stochastic Bilevel Optimizationcited by 11
  8. 2021Long Random Matrices and Tensor Unfoldingcited by 10
  9. 2024Guaranteed Nonconvex Factorization Approach for Tensor Train Recoverycited by 8
  10. 2021Learning Good State and Action Representations via Tensor Decompositioncited by 7
  11. 2021Tensor Principal Component Analysis in High Dimensional CP Modelscited by 7
  12. 2023Deflated HeteroPCA: Overcoming the curse of ill-conditioning in heteroskedastic PCAcited by 7
27 more
  1. 2023Provably Accelerating Ill-Conditioned Low-rank Estimation via Scaled Gradient Descent, Even with Overparameterizationcited by 6
  2. 2022Optimal Clustering by Lloyd Algorithm for Low-Rank Mixture Modelcited by 5
  3. 2023On High-dimensional and Low-rank Tensor Banditscited by 5
  4. 2021Beyond the Signs: Nonparametric Tensor Completion via Sign Seriescited by 4
  5. 2022Multiway Spherical Clustering via Degree-Corrected Tensor Block Modelscited by 4
  6. 2024Computational and Statistical Guarantees for Tensor-on-Tensor Regression with Tensor Train Decompositioncited by 4
  7. 2025A Scalable Factorization Approach for High-Order Structured Tensor Recoverycited by 4
  8. 2024Sharp Analysis of Power Iteration for Tensor PCAcited by 2
  9. 2024Robust Low-rank Tensor Train Recoverycited by 2
  10. 2022Multivariate Analysis for Multiple Network Data via Semi-Symmetric Tensor PCAcited by 1
  11. 2023Mode-wise Principal Subspace Pursuit and Matrix Spiked Covariance Modelcited by 1
  12. 2023Convergence Analysis for Learning Orthonormal Deep Linear Neural Networkscited by 1
  13. 2024Tensor Methods in High Dimensional Data Analysis: Opportunities and Challengescited by 1
  14. 2022Efficient Estimation for Longitudinal Networks via Adaptive Mergingcited by 0
  15. 2023Statistical and computational rates in high rank tensor estimationcited by 0
  16. 2025Federated Low-Rank Tensor Estimation for Multimodal Image Reconstructioncited by 0
  17. 2025Accelerating Large-Scale Regularized High-Order Tensor Recoverycited by 0
  18. 2025Optimal Bias-variance Tradeoff in Matrix and Tensor Estimationcited by 0
  19. 2025Guaranteed Noisy CP Tensor Recovery via Riemannian Optimization on the Segre Manifoldcited by 0
  20. 2025Near-Efficient and Non-Asymptotic Multiway Inferencecited by 0
  21. 2025Tensor Computing Interface: An Application-Oriented, Lightweight Interface for Portable High-Performance Tensor Network Applicationscited by 0
  22. 2026Multi-Dimensional Visual Data Recovery: Scale-Aware Tensor Modeling and Accelerated Randomized Computationcited by 0
  23. 2026Robust Tensor Regression with Nonconvexity: Algorithmic and Statistical Theorycited by 0
  24. 2026Dual-Channel Tensor Neural Networks: Finite-Sample Theory and Conformal Structure Selectioncited by 0
  25. 2026Structured Adaptive Tensor Prediction for Streaming Datacited by 0
  26. 2026Precise sample covariance spectral norm error -- an RDT viewcited by 0
  27. 2026Heteroskedastic Canonical Polyadic Tensor Decompositioncited by 0