# Transfer Learning with Random Coefficient Ridge Regression

arXiv: https://arxiv.org/abs/2306.15915 · HTML: https://mlsanity.com/paper/2306.15915/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 26 references that are in the map.
- First posted on arXiv 28 Jun 2023.

## Builds on (most cited first, 9 of 9)

- [Surprises in High-Dimensional Ridgeless Least Squares Interpolation](https://mlsanity.com/paper/1903.08560/) (2019)
- [Deep Convolutional Neural Networks for Computer-Aided Detection: CNN Architectures, Dataset Characteristics and Transfer Learning](https://mlsanity.com/paper/1602.03409/) (2016)
- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [On the Optimal Weighted ℓ2 Regularization in Overparameterized Linear Regression](https://mlsanity.com/paper/2006.05800/) (2020)
- [Transfer Learning for High-dimensional Linear Regression: Prediction, Estimation, and Minimax Optimality](https://mlsanity.com/paper/2006.10593/) (2020)
- [Asymptotics of Ridge (less) Regression under General Source Condition](https://mlsanity.com/paper/2006.06386/) (2020)
- [Dimension free ridge regression](https://mlsanity.com/paper/2210.08571/) (2022)
- [WONDER: Weighted one-shot distributed ridge regression in high dimensions](https://mlsanity.com/paper/1903.09321/) (2019)
- [Cross-trait prediction accuracy of high-dimensional ridge-type estimators in genome-wide association studies](https://mlsanity.com/paper/1911.10142/) (2019)

## Built on by (most cited first, 2 of 2)

- [Transfer learning via Regularized Linear Discriminant Analysis](https://mlsanity.com/paper/2501.02411/) (2025)
- [High-Dimensional Asymptotics and Dataset Selection for Private Transfer Learning](https://mlsanity.com/paper/2610.02578/) (2026)

## Abstract (arXiv)

Ridge regression with random coefficients provides an important alternative to fixed coefficients regression in high dimensional setting when the effects are expected to be small but not zeros. This paper considers estimation and prediction of random coefficient ridge regression in the setting of transfer learning, where in addition to observations from the target model, source samples from different but possibly related regression models are available. The informativeness of the source model to the target model can be quantified by the correlation between the regression coefficients. This paper proposes two estimators of regression coefficients of the target model as the weighted sum of the ridge estimates of both target and source models, where the weights can be determined by minimizing the empirical estimation risk or prediction risk. Using random matrix theory, the limiting values of the optimal weights are derived under the setting when p/n rightarrow γ, where p is the number of the predictors and n is the sample size, which leads to an explicit expression of the estimation or prediction risks. Simulations show that these limiting risks agree very well with the empirical risks. An application to predicting the polygenic risk scores for lipid traits shows such transfer learning methods lead to smaller prediction errors than the single sample ridge regression or Lasso-based transfer learning.