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Transfer Learning for Matrix Completion

arXiv 2507.02248 ↗First posted 3 Jul 2025stat.ML cs.LGcited by 0

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Abstract (arXiv)

In this paper, we explore the knowledge transfer under the setting of matrix completion, which aims to enhance the estimation of a low-rank target matrix with auxiliary data available. We propose a transfer learning procedure given prior information on which source datasets are favorable. We study its convergence rates and prove its minimax optimality. Our analysis reveals that with the source matrices close enough to the target matrix, out method outperforms the traditional method using the single target data. In particular, we leverage the advanced sharp concentration inequalities introduced in citebrailovskaya2024universality to eliminate a logarithmic factor in the convergence rate, which is crucial for proving the minimax optimality. When the relevance of source datasets is unknown, we develop an efficient detection procedure to identify informative sources and establish its selection consistency. Simulations and real data analysis are conducted to support the validity of our methodology.

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 23 of its 63 references that are in the map. First posted on arXiv 3 Jul 2025.

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References · 23

  1. 2019Parameter-Efficient Transfer Learning for NLPcited by 4,195
  2. 2019A Comprehensive Survey on Transfer Learningcited by 1,154
  3. 2018A Survey on Deep Transfer Learningcited by 417
  4. 2020Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimalitycited by 89
  5. 2021Transfer Learning under High-dimensional Generalized Linear Modelscited by 69
  6. 2019Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifiercited by 64
  7. 2020Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Controlcited by 38
  8. 2017Transfer learning for music classification and regression taskscited by 36
  9. 2022Transfer Learning for Contextual Multi-armed Banditscited by 24
  10. 2024Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedurecited by 19
  11. 2016Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entriescited by 18
  12. 2022Robust angle-based transfer learning in high dimensionscited by 16
11 more
  1. 2024TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regressioncited by 11
  2. 2018Collective Matrix Completioncited by 9
  3. 2024Transfer Learning with General Estimating Equationscited by 6
  4. 2023Robust Transfer Learning with Unreliable Source Datacited by 4
  5. 2020Matrix Completion Methods for the Total Electron Content Video Reconstructioncited by 3
  6. 2023Dynamic Matrix Recoverycited by 3
  7. 2024Representational Transfer Learning for Matrix Completioncited by 3
  8. 2024LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimationcited by 3
  9. 2023Simultaneous Estimation and Dataset Selection for Transfer Learning in High Dimensions by a Non-convex Penaltycited by 2
  10. 2024Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimationcited by 2
  11. 2025Optimal Transfer Learning for Missing Not-at-Random Matrix Completioncited by 2

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