# Unified Transfer Learning Models in High-Dimensional Linear Regression

arXiv: https://arxiv.org/abs/2307.00238 · HTML: https://mlsanity.com/paper/2307.00238/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 31 references that are in the map.
- First posted on arXiv 1 Jul 2023.

## Builds on (most cited first, 10 of 10)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [On the Theory of Transfer Learning: The Importance of Task Diversity](https://mlsanity.com/paper/2006.11650/) (2020)
- [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)
- [Regularized M-estimators with nonconvexity: Statistical and algorithmic theory for local optima](https://mlsanity.com/paper/1305.2436/) (2013)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Regression modeling on stratified data with the lasso](https://mlsanity.com/paper/1508.05476/) (2015)
- [Multiple-Splitting Projection Test for High-Dimensional Mean Vectors](https://mlsanity.com/paper/2110.15480/) (2021)
- [Adaptive Weighted Multi-View Clustering](https://mlsanity.com/paper/2110.13240/) (2021)
- [Tests for High Dimensional Generalized Linear Models](https://mlsanity.com/paper/1402.4882/) (2014)

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

- [TransFusion: Covariate-Shift Robust Transfer Learning for High-Dimensional Regression](https://mlsanity.com/paper/2404.01153/) (2024)
- [AdaTrans: Feature-wise and Sample-wise Adaptive Transfer Learning for High-dimensional Regression](https://mlsanity.com/paper/2403.13565/) (2024)
- [Trans-Glasso: A Transfer Learning Approach to Precision Matrix Estimation](https://mlsanity.com/paper/2411.15624/) (2024)

## Abstract (arXiv)

Transfer learning plays a key role in modern data analysis when: (1) the target data are scarce but the source data are sufficient; (2) the distributions of the source and target data are heterogeneous. This paper develops an interpretable unified transfer learning model, termed as UTrans, which can detect both transferable variables and source data. More specifically, we establish the estimation error bounds and prove that our bounds are lower than those with target data only. Besides, we propose a source detection algorithm based on hypothesis testing to exclude the nontransferable data. We evaluate and compare UTrans to the existing algorithms in multiple experiments. It is shown that UTrans attains much lower estimation and prediction errors than the existing methods, while preserving interpretability. We finally apply it to the US intergenerational mobility data and compare our proposed algorithms to the classical machine learning algorithms.