mlsanityData to 14 Oct 2026

A Max-Norm Constrained Minimization Approach to 1-Bit Matrix Completion

arXiv 1309.6013 ↗First posted 24 Sep 2013stat.ML math.ST stat.THcited by 25

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Abstract (arXiv)

We consider in this paper the problem of noisy 1-bit matrix completion under a general non-uniform sampling distribution using the max-norm as a convex relaxation for the rank. A max-norm constrained maximum likelihood estimate is introduced and studied. The rate of convergence for the estimate is obtained. Information-theoretical methods are used to establish a minimax lower bound under the general sampling model. The minimax upper and lower bounds together yield the optimal rate of convergence for the Frobenius norm loss. Computational algorithms and numerical performance are also discussed.

Key facts. Cited by 25 papers in the map (data through 14 Oct 2026). First posted on arXiv 24 Sep 2013.

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Citing papers per year: 2021: 4; 2022: 4; 2023: 7; 2024: 6; 2025: 1; 2026: 3.

25 papers.

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  1. 2022High Dimensional Statistical Estimation under Uniformly Dithered One-bit Quantizationcited by 13
  2. 2022Quantizing Heavy-tailed Data in Statistical Estimation: (Near) Minimax Rates, Covariate Quantization, and Uniform Recoverycited by 9
  3. 2021TenIPS: Inverse Propensity Sampling for Tensor Completioncited by 7
  4. 2024Concentration properties of fractional posterior in 1-bit matrix completioncited by 7
  5. 2021Matrix Completion with Model-free Weightingcited by 6
  6. 2023Quantized Radio Map Estimation Using Tensor and Deep Generative Modelscited by 6
  7. 2023Quantized Low-Rank Multivariate Regression with Random Ditheringcited by 5
  8. 2022Tensor Completion with Provable Consistency and Fairness Guarantees for Recommender Systemscited by 4
  9. 2023A Majorization-Minimization Gauss-Newton Method for 1-Bit Matrix Completioncited by 2
  10. 2024Causal Customer Churn Analysis with Low-rank Tensor Block Hazard Modelcited by 2
  11. 2022A Generalized Latent Factor Model Approach to Mixed-data Matrix Completion with Entrywise Consistencycited by 1
  12. 2023Transductive Matrix Completion with Calibration for Multi-Task Learningcited by 1
13 more
  1. 2024Collaborative Automotive Radar Sensing via Mixed-Precision Distributed Array Completioncited by 1
  2. 2024Data Imputation by Pursuing Better Classification: A Supervised Kernel-Based Methodcited by 1
  3. 2024Impossibility of latent inner product recovery via rate distortioncited by 1
  4. 2021Maximum a Posteriori Inference of Random Dot Product Graphs via Conic Programmingcited by 0
  5. 2021One-Bit Matrix Completion with Differential Privacycited by 0
  6. 2023An Admissible Shift-Consistent Method for Recommender Systemscited by 0
  7. 2023Matrix Completion from One-Bit Dither Samplescited by 0
  8. 2023Misclassification excess risk bounds for 1-bit matrix completioncited by 0
  9. 2024Convergence of the majorized PAM method with subspace correction for low-rank composite factorization modelcited by 0
  10. 2025Pairwise Comparisons without Stochastic Transitivity: Model, Theory and Applicationscited by 0
  11. 2026An Interpretable and Scalable Framework for Evaluating Large Language Modelscited by 0
  12. 2026Empirical Bayes 1-bit matrix completioncited by 0
  13. 2026Exponential-Family Tensor Completion via Nonconvex Dual Total-Variation Regularizationcited by 0