mlsanityData to 7 Oct 2026

Matrix Completion and Low-Rank SVD via Fast Alternating Least Squares

arXiv 1410.2596 ↗First posted 9 Oct 2014stat.ME stat.MLcited by 104

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Abstract (arXiv)

The matrix-completion problem has attracted a lot of attention, largely as a result of the celebrated Netflix competition. Two popular approaches for solving the problem are nuclear-norm-regularized matrix approximation (Candes and Tao, 2009, Mazumder, Hastie and Tibshirani, 2010), and maximum-margin matrix factorization (Srebro, Rennie and Jaakkola, 2005). These two procedures are in some cases solving equivalent problems, but with quite different algorithms. In this article we bring the two approaches together, leading to an efficient algorithm for large matrix factorization and completion that outperforms both of these. We develop a software package "softImpute" in R for implementing our approaches, and a distributed version for very large matrices using the "Spark" cluster programming environment.

Key facts. Cited by 104 papers in the map (data through 7 Oct 2026). First posted on arXiv 9 Oct 2014.

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Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 17; 2022: 15; 2023: 15; 2024: 24; 2025: 18; 2026: 15.

104 papers.

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  1. 2022HyperImpute: Generalized Iterative Imputation with Automatic Model Selectioncited by 81
  2. 2023Generating and Imputing Tabular Data via Diffusion and Flow-based Gradient-Boosted Treescited by 60
  3. 2021Causal Matrix Completioncited by 45
  4. 2023ReMasker: Imputing Tabular Data with Masked Autoencodingcited by 35
  5. 2023Transformed Distribution Matching for Missing Value Imputationcited by 31
  6. 2024DiffPuter: Empowering Diffusion Models for Missing Data Imputationcited by 17
  7. 2021Multiple Imputation via Generative Adversarial Network for High-dimensional Blockwise Missing Value Problemscited by 15
  8. 2022Data Imputation with Iterative Graph Reconstructioncited by 15
  9. 2021Smooth Bilevel Programming for Sparse Regularizationcited by 14
  10. 2022Numerical Optimizations for Weighted Low-rank Estimation on Language Modelcited by 14
  11. 2024On Speeding Up Language Model Evaluationcited by 14
  12. 2025Deep Weight Factorization: Sparse Learning Through the Lens of Artificial Symmetriescited by 13
38 more
  1. 2022Handling Missing Data via Max-Entropy Regularized Graph Autoencodercited by 12
  2. 2022Randomly Initialized Alternating Least Squares: Fast Convergence for Matrix Sensingcited by 11
  3. 2022Smooth over-parameterized solvers for non-smooth structured optimizationcited by 11
  4. 2021Multi-source Learning via Completion of Block-wise Overlapping Noisy Matricescited by 10
  5. 2022Efficient Nearest Neighbor Search for Cross-Encoder Models using Matrix Factorizationcited by 10
  6. 2023Recursive Video Lane Detectioncited by 9
  7. 2021Fairness in Missing Data Imputationcited by 8
  8. 2021Matrix Completion with Model-free Weightingcited by 6
  9. 2024A Context-Aware Approach for Enhancing Data Imputation with Pre-trained Language Modelscited by 5
  10. 2024Explainability of Machine Learning Models under Missing Datacited by 5
  11. 2021Low-rank Matrix Recovery With Unknown Correspondencecited by 4
  12. 2023AmGCL: Feature Imputation of Attribute Missing Graph via Self-supervised Contrastive Learningcited by 4
  13. 2024Unmasking Trees for Tabular Datacited by 4
  14. 2021Wasserstein Graph Neural Networks for Graphs with Missing Attributescited by 3
  15. 2022Multiple Imputation with Neural Network Gaussian Process for High-dimensional Incomplete Datacited by 3
  16. 2023Numerical Data Imputation for Multimodal Data Sets: A Probabilistic Nearest-Neighbor Kernel Density Approachcited by 3
  17. 2024Asymptotic Dynamics of Alternating Minimization for Bilinear Regressioncited by 3
  18. 2024Online Policy Learning and Inference by Matrix Completioncited by 3
  19. 2024On the Low-Rank Parametrization of Reward Models for Controlled Language Generationcited by 3
  20. 2025Incomplete Graph Learning: A Comprehensive Surveycited by 3
  21. 2025CACTI: Leveraging Copy Masking and Contextual Information to Improve Tabular Data Imputationcited by 3
  22. 2021The Power of Subsampling in Submodular Maximizationcited by 2
  23. 2021How Low Can We Go: Trading Memory for Error in Low-Precision Trainingcited by 2
  24. 2021Weighted Low-Rank Matrix Approximation: Acceleration and Applicationscited by 2
  25. 2022Principal Component Analysis based frameworks for efficient missing data imputation algorithmscited by 2
  26. 2023Conditional expectation with regularization for missing data imputationcited by 2
  27. 2023Adversarial Learning for Feature Shift Detection and Correctioncited by 2
  28. 2024Causal Imputation for Counterfactual SCMs: Bridging Graphs and Latent Factor Modelscited by 2
  29. 2024Statistical Inference For Noisy Matrix Completion Incorporating Auxiliary Informationcited by 2
  30. 2024RE-RecSys: An End-to-End system for recommending properties in Real-Estate domaincited by 2
  31. 2024Learning Counterfactual Distributions via Kernel Nearest Neighborscited by 2
  32. 2025Representation Learning of Lab Values via Masked AutoEncoderscited by 2
  33. 2025Missing Data in Signal Processing and Machine Learning: Models, Methods and Modern Approachescited by 2
  34. 2025One Pipeline, Many Transformers: Pattern-Specific Imputation Specialists for Tabular Missing Datacited by 2
  35. 2026Large Language Models for Missing Data Imputation: Understanding Behavior, Hallucination Effects, and Control Mechanismscited by 2
  36. 2026SYN-DIGITS: A Synthetic Control Framework for Calibrated Digital Twin Simulationcited by 2
  37. 2021NoisyCUR: An algorithm for two-cost budgeted matrix completioncited by 1
  38. 2021Dimension Reduction for Data with Heterogeneous Missingnesscited by 1

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