# Representational Transfer Learning for Matrix Completion

arXiv: https://arxiv.org/abs/2412.06233 · HTML: https://mlsanity.com/paper/2412.06233/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 48 references that are in the map.
- First posted on arXiv 9 Dec 2024.

## Builds on (most cited first, 6 of 6)

- [Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness](https://mlsanity.com/paper/2303.17765/) (2023)
- [A Unified Computational and Statistical Framework for Nonconvex Low-Rank Matrix Estimation](https://mlsanity.com/paper/1610.05275/) (2016)
- [Transfer Learning with General Estimating Equations](https://mlsanity.com/paper/2410.04398/) (2024)
- [Knowledge Transfer across Multiple Principal Component Analysis Studies](https://mlsanity.com/paper/2403.07431/) (2024)
- [Representation Transfer Learning for Semiparametric Regression](https://mlsanity.com/paper/2406.13197/) (2024)
- [Simultaneous Estimation and Dataset Selection for Transfer Learning in High Dimensions by a Non-convex Penalty](https://mlsanity.com/paper/2306.04182/) (2023)

## Built on by (most cited first, 4 of 4)

- [LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation](https://mlsanity.com/paper/2412.20605/) (2024)
- [Optimal Transfer Learning for Missing Not-at-Random Matrix Completion](https://mlsanity.com/paper/2503.00174/) (2025)
- [SMART: A Spectral Transfer Approach to Multi-Task Learning](https://mlsanity.com/paper/2604.20161/) (2026)
- [Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2507.02248/) (2025)

## Abstract (arXiv)

We propose to transfer representational knowledge from multiple sources to a target noisy matrix completion task by aggregating singular subspaces information. Under our representational similarity framework, we first integrate linear representation information by solving a two-way principal component analysis problem based on a properly debiased matrix-valued dataset. After acquiring better column and row representation estimators from the sources, the original high-dimensional target matrix completion problem is then transformed into a low-dimensional linear regression, of which the statistical efficiency is guaranteed. A variety of extensional arguments, including post-transfer statistical inference and robustness against negative transfer, are also discussed alongside. Finally, extensive simulation results and a number of real data cases are reported to support our claims.