# Data-Driven Subgroup Identification for Linear Regression

arXiv: https://arxiv.org/abs/2305.00195 · HTML: https://mlsanity.com/paper/2305.00195/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 37 references that are in the map.
- First posted on arXiv 29 Apr 2023.

## Builds on (most cited first, 13 of 13)

- [Consistent Estimators for Learning to Defer to an Expert](https://mlsanity.com/paper/2006.01862/) (2020)
- [Predict Responsibly: Improving Fairness and Accuracy by Learning to Defer](https://mlsanity.com/paper/1711.06664/) (2017)
- [Learning from Untrusted Data](https://mlsanity.com/paper/1611.02315/) (2016)
- [Towards Unbiased and Accurate Deferral to Multiple Experts](https://mlsanity.com/paper/2102.13004/) (2021)
- [List-Decodable Linear Regression](https://mlsanity.com/paper/1905.05679/) (2019)
- [List Decodable Learning via Sum of Squares](https://mlsanity.com/paper/1905.04660/) (2019)
- [How to Learn when Data Gradually Reacts to Your Model](https://mlsanity.com/paper/2112.07042/) (2021)
- [Piecewise Linear Regression via a Difference of Convex Functions](https://mlsanity.com/paper/2007.02422/) (2020)
- [Optimal Non-Asymptotic Lower Bound on the Minimax Regret of Learning with Expert Advice](https://mlsanity.com/paper/1511.02176/) (2015)
- [Tight Hardness Results for Maximum Weight Rectangles](https://mlsanity.com/paper/1602.05837/) (2016)
- [Conditional Sparse Linear Regression](https://mlsanity.com/paper/1608.05152/) (2016)
- [Conditional Linear Regression](https://mlsanity.com/paper/1806.02326/) (2018)
- [Efficient Algorithms for Multidimensional Segmented Regression](https://mlsanity.com/paper/2003.11086/) (2020)

## Built on by (most cited first, 6 of 6)

- [The Data Addition Dilemma](https://mlsanity.com/paper/2408.04154/) (2024)
- [Learning Exceptional Subgroups by End-to-End Maximizing KL-divergence](https://mlsanity.com/paper/2402.12930/) (2024)
- [Intersectional Unfairness Discovery](https://mlsanity.com/paper/2405.20790/) (2024)
- [Personalized Prediction By Learning Halfspace Reference Classes Under Well-Behaved Distribution](https://mlsanity.com/paper/2509.15592/) (2025)
- [Contrasting Global and Patient-Specific Regression Models via a Neural Network Representation](https://mlsanity.com/paper/2601.18658/) (2026)
- [Subgroup Discovery with the Cox Model](https://mlsanity.com/paper/2512.20762/) (2025)

## Abstract (arXiv)

Medical studies frequently require to extract the relationship between each covariate and the outcome with statistical confidence measures. To do this, simple parametric models are frequently used (e.g. coefficients of linear regression) but usually fitted on the whole dataset. However, it is common that the covariates may not have a uniform effect over the whole population and thus a unified simple model can miss the heterogeneous signal. For example, a linear model may be able to explain a subset of the data but fail on the rest due to the nonlinearity and heterogeneity in the data. In this paper, we propose DDGroup (data-driven group discovery), a data-driven method to effectively identify subgroups in the data with a uniform linear relationship between the features and the label. DDGroup outputs an interpretable region in which the linear model is expected to hold. It is simple to implement and computationally tractable for use. We show theoretically that, given a large enough sample, DDGroup recovers a region where a single linear model with low variance is well-specified (if one exists), and experiments on real-world medical datasets confirm that it can discover regions where a local linear model has improved performance. Our experiments also show that DDGroup can uncover subgroups with qualitatively different relationships which are missed by simply applying parametric approaches to the whole dataset.