# Transfer learning via Regularized Linear Discriminant Analysis

arXiv: https://arxiv.org/abs/2501.02411 · HTML: https://mlsanity.com/paper/2501.02411/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 30 references that are in the map.
- First posted on arXiv 5 Jan 2025.

## Builds on (most cited first, 12 of 12)

- [High-Dimensional Asymptotics of Prediction: Ridge Regression and Classification](https://mlsanity.com/paper/1507.03003/) (2015)
- [A survey on domain adaptation theory: learning bounds and theoretical guarantees](https://mlsanity.com/paper/2004.11829/) (2020)
- [A Survey of Deep Meta-Learning](https://mlsanity.com/paper/2010.03522/) (2020)
- [Transfer Learning for Nonparametric Classification: Minimax Rate and Adaptive Classifier](https://mlsanity.com/paper/1906.02903/) (2019)
- [Covariate Shift in High-Dimensional Random Feature Regression](https://mlsanity.com/paper/2111.08234/) (2021)
- [Distributed linear regression by averaging](https://mlsanity.com/paper/1810.00412/) (2018)
- [Generalization error of min-norm interpolators in transfer learning](https://mlsanity.com/paper/2406.13944/) (2024)
- [A Comprehensive Overview and Survey of Recent Advances in Meta-Learning](https://mlsanity.com/paper/2004.11149/) (2020)
- [WONDER: Weighted one-shot distributed ridge regression in high dimensions](https://mlsanity.com/paper/1903.09321/) (2019)
- [Minimax And Adaptive Transfer Learning for Nonparametric Classification under Distributed Differential Privacy Constraints](https://mlsanity.com/paper/2406.20088/) (2024)
- [Approximately optimal domain adaptation with Fisher's Linear Discriminant](https://mlsanity.com/paper/2302.14186/) (2023)
- [Transfer Learning with Random Coefficient Ridge Regression](https://mlsanity.com/paper/2306.15915/) (2023)

## Built on by (most cited first, 1 of 1)

- [Transfer Learning for Linear Discriminant Analysis with a Shared Classification Signal](https://mlsanity.com/paper/2607.06936/) (2026)

## Abstract (arXiv)

Linear discriminant analysis is a widely used method for classification. However, the high dimensionality of predictors combined with small sample sizes often results in large classification errors. To address this challenge, it is crucial to leverage data from related source models to enhance the classification performance of a target model. We propose to address this problem in the framework of transfer learning. In this paper, we present novel transfer learning methods via regularized random-effects linear discriminant analysis, where the discriminant direction is estimated as a weighted combination of ridge estimates obtained from both the target and source models. Multiple strategies for determining these weights are introduced and evaluated, including one that minimizes the estimation risk of the discriminant vector and another that minimizes the classification error. Utilizing results from random matrix theory, we explicitly derive the asymptotic values of these weights and the associated classification error rates in the high-dimensional setting, where p/n rightarrow γ, with p representing the predictor dimension and n the sample size. We also provide geometric interpretations of various weights and a guidance on which weights to choose. Extensive numerical studies, including simulations and analysis of proteomics-based 10-year cardiovascular disease risk classification, demonstrate the effectiveness of the proposed approach.