# Optimal Downsampling for Imbalanced Classification with Generalized Linear Models

arXiv: https://arxiv.org/abs/2410.08994 · HTML: https://mlsanity.com/paper/2410.08994/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 54 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 8 of 8)

- [Convex Optimization: Algorithms and Complexity](https://mlsanity.com/paper/1405.4980/) (2014)
- [Imbalanced-learn: A Python Toolbox to Tackle the Curse of Imbalanced Datasets in Machine Learning](https://mlsanity.com/paper/1609.06570/) (2016)
- [A Model of Double Descent for High-dimensional Binary Linear Classification](https://mlsanity.com/paper/1911.05822/) (2019)
- [The Complexity of Making the Gradient Small in Stochastic Convex Optimization](https://mlsanity.com/paper/1902.04686/) (2019)
- [On the proliferation of support vectors in high dimensions](https://mlsanity.com/paper/2009.10670/) (2020)
- [Local case-control sampling: Efficient subsampling in imbalanced data sets](https://mlsanity.com/paper/1306.3706/) (2013)
- [Logistic Regression for Massive Data with Rare Events](https://mlsanity.com/paper/2006.00683/) (2020)
- [Fast Imbalanced Classification of Healthcare Data with Missing Values](https://mlsanity.com/paper/1503.06250/) (2015)

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

- [Concentration and excess risk bounds for imbalanced classification with synthetic oversampling](https://mlsanity.com/paper/2510.20472/) (2025)
- [CrediBench: Building Web-Scale Network Datasets for Information Integrity](https://mlsanity.com/paper/2509.23340/) (2025)

## Abstract (arXiv)

Downsampling or under-sampling is a technique that is utilized in the context of large and highly imbalanced classification models. We study optimal downsampling for imbalanced classification using generalized linear models (GLMs). We propose a pseudo maximum likelihood estimator and study its asymptotic normality in the context of increasingly imbalanced populations relative to an increasingly large sample size. We provide theoretical guarantees for the introduced estimator. Additionally, we compute the optimal downsampling rate using a criterion that balances statistical accuracy and computational efficiency. Our numerical experiments, conducted on both synthetic and empirical data, further validate our theoretical results, and demonstrate that the introduced estimator outperforms commonly available alternatives.