# LEARNER: A Transfer Learning Method for Low-Rank Matrix Estimation

arXiv: https://arxiv.org/abs/2412.20605 · HTML: https://mlsanity.com/paper/2412.20605/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 48 references that are in the map.
- First posted on arXiv 29 Dec 2024.

## Builds on (most cited first, 16 of 16)

- [No Spurious Local Minima in Nonconvex Low Rank Problems: A Unified Geometric Analysis](https://mlsanity.com/paper/1704.00708/) (2017)
- [Matrix Completion has No Spurious Local Minimum](https://mlsanity.com/paper/1605.07272/) (2016)
- [Inference and Uncertainty Quantification for Noisy Matrix Completion](https://mlsanity.com/paper/1906.04159/) (2019)
- [Heteroskedastic PCA: Algorithm, Optimality, and Applications](https://mlsanity.com/paper/1810.08316/) (2018)
- [Understanding Alternating Minimization for Matrix Completion](https://mlsanity.com/paper/1312.0925/) (2013)
- [Learning from Similar Linear Representations: Adaptivity, Minimaxity, and Robustness](https://mlsanity.com/paper/2303.17765/) (2023)
- [Inference for Heteroskedastic PCA with Missing Data](https://mlsanity.com/paper/2107.12365/) (2021)
- [Targeting Underrepresented Populations in Precision Medicine: A Federated Transfer Learning Approach](https://mlsanity.com/paper/2108.12112/) (2021)
- [Personalized PCA: Decoupling Shared and Unique Features](https://mlsanity.com/paper/2207.08041/) (2022)
- [ScreeNOT: Exact MSE-Optimal Singular Value Thresholding in Correlated Noise](https://mlsanity.com/paper/2009.12297/) (2020)
- [The Non-convex Geometry of Low-rank Matrix Optimization](https://mlsanity.com/paper/1611.03060/) (2016)
- [Group-Sparse Matrix Factorization for Transfer Learning of Word Embeddings](https://mlsanity.com/paper/2104.08928/) (2021)
- [Target PCA: Transfer Learning Large Dimensional Panel Data](https://mlsanity.com/paper/2308.15627/) (2023)
- [Inference of Dependency Knowledge Graph for Electronic Health Records](https://mlsanity.com/paper/2312.15611/) (2023)
- [Knowledge Transfer across Multiple Principal Component Analysis Studies](https://mlsanity.com/paper/2403.07431/) (2024)
- [Representational Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2412.06233/) (2024)

## Built on by (most cited first, 3 of 3)

- [Optimal Transfer Learning for Missing Not-at-Random Matrix Completion](https://mlsanity.com/paper/2503.00174/) (2025)
- [Transfer Learning for Matrix Completion](https://mlsanity.com/paper/2507.02248/) (2025)
- [Generalization Bounds for Semi-supervised Matrix Completion with Distributional Side Information](https://mlsanity.com/paper/2511.13049/) (2025)

## Abstract (arXiv)

Low-rank matrix estimation is a fundamental problem in statistics and machine learning with applications across biomedical sciences, including genetics, medical imaging, drug discovery, and electronic health record data analysis. In the context of heterogeneous data generated from diverse sources, a key challenge lies in leveraging data from a source population to enhance the estimation of a low-rank matrix in a target population of interest. We propose an approach that leverages similarity in the latent row and column spaces between the source and target populations to improve estimation in the target population, which we refer to as LatEnt spAce-based tRaNsfer lEaRning (LEARNER). LEARNER is based on performing a low-rank approximation of the target population data which penalizes differences between the latent row and column spaces between the source and target populations. We present a cross-validation approach that allows the method to adapt to the degree of heterogeneity across populations. We conducted extensive simulations which found that LEARNER often outperforms the benchmark approach that only uses the target population data, especially as the signal-to-noise ratio in the source population increases. We also performed an illustrative application and empirical comparison of LEARNER and benchmark approaches in a re-analysis of summary statistics from a genome-wide association study in the BioBank Japan cohort. LEARNER is implemented in the R package learner and the Python package learner-py.