# Transfer Learning for Matrix Completion

arXiv: https://arxiv.org/abs/2507.02248 · HTML: https://mlsanity.com/paper/2507.02248/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 23 of its 63 references that are in the map.
- First posted on arXiv 3 Jul 2025.

## Builds on (most cited first, 23 of 23)

- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [A Survey on Deep Transfer Learning](https://mlsanity.com/paper/1808.01974/) (2018)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Transfer Learning under High-dimensional Generalized Linear Models](https://mlsanity.com/paper/2105.14328/) (2021)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Transfer Learning in Large-scale Gaussian Graphical Models with False Discovery Rate Control](https://mlsanity.com/paper/2010.11037/) (2020)
- [Transfer learning for music classification and regression tasks](https://mlsanity.com/paper/1703.09179/) (2017)
- [Transfer Learning for Contextual Multi-armed Bandits](https://mlsanity.com/paper/2211.12612/) (2022)
- [Transfer Learning for Nonparametric Regression: Non-asymptotic Minimax Analysis and Adaptive Procedure](https://mlsanity.com/paper/2401.12272/) (2024)
- [Sub-Gaussian estimators of the mean of a random matrix with heavy-tailed entries](https://mlsanity.com/paper/1605.07129/) (2016)
- [Robust angle-based transfer learning in high dimensions](https://mlsanity.com/paper/2210.12759/) (2022)
- [TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression](https://mlsanity.com/paper/2404.01153/) (2024)
- [Collective Matrix Completion](https://mlsanity.com/paper/1807.09010/) (2018)
- [Transfer Learning with General Estimating Equations](https://mlsanity.com/paper/2410.04398/) (2024)
- [Robust Transfer Learning with Unreliable Source Data](https://mlsanity.com/paper/2310.04606/) (2023)
- [Representational Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2412.06233/) (2024)
- [Matrix Completion Methods for the Total Electron Content Video Reconstruction](https://mlsanity.com/paper/2012.01618/) (2020)
- [Dynamic Matrix Recovery](https://mlsanity.com/paper/2305.10524/) (2023)
- [LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation](https://mlsanity.com/paper/2412.20605/) (2024)
- [Simultaneous Estimation and Dataset Selection for Transfer Learning in High Dimensions by a Non-convex Penalty](https://mlsanity.com/paper/2306.04182/) (2023)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)
- [Optimal Transfer Learning for Missing Not-at-Random Matrix Completion](https://mlsanity.com/paper/2503.00174/) (2025)

## 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.