# Transfer-Learning Across Datasets with Different Input Dimensions: An Algorithm and Analysis for the Linear Regression Case

arXiv: https://arxiv.org/abs/2202.05069 · HTML: https://mlsanity.com/paper/2202.05069/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 27 references that are in the map.
- First posted on arXiv 10 Feb 2022.

## Builds on (most cited first, 7 of 7)

- [A Comprehensive Survey on Transfer Learning](https://mlsanity.com/paper/1911.02685/) (2019)
- [Return of Frustratingly Easy Domain Adaptation](https://mlsanity.com/paper/1511.05547/) (2015)
- [On the Value of Target Data in Transfer Learning](https://mlsanity.com/paper/2002.04747/) (2020)
- [Minimax Lower Bounds for Transfer Learning with Linear and One-hidden Layer Neural Networks](https://mlsanity.com/paper/2006.10581/) (2020)
- [Learning with Feature Evolvable Streams](https://mlsanity.com/paper/1706.05259/) (2017)
- [Transfer Learning for Linear Regression: a Statistical Test of Gain](https://mlsanity.com/paper/2102.09504/) (2021)
- [Data enriched linear regression](https://mlsanity.com/paper/1304.1837/) (2013)

## Abstract (arXiv)

With the development of new sensors and monitoring devices, more sources of data become available to be used as inputs for machine learning models. These can on the one hand help to improve the accuracy of a model. On the other hand, combining these new inputs with historical data remains a challenge that has not yet been studied in enough detail. In this work, we propose a transfer learning algorithm that combines new and historical data with different input dimensions. This approach is easy to implement, efficient, with computational complexity equivalent to the ordinary least-squares method, and requires no hyperparameter tuning, making it straightforward to apply when the new data is limited. Different from other approaches, we provide a rigorous theoretical study of its robustness, showing that it cannot be outperformed by a baseline that utilizes only the new data. Our approach achieves state-of-the-art performance on 9 real-life datasets, outperforming the linear DSFT, another linear transfer learning algorithm, and performing comparably to non-linear DSFT.