# Local case-control sampling: Efficient subsampling in imbalanced data sets

arXiv: https://arxiv.org/abs/1306.3706 · HTML: https://mlsanity.com/paper/1306.3706/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Jun 2013.

## Built on by (most cited first, 14 of 14)

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- [On feature selection in double-imbalanced data settings: a Random Forest approach](https://mlsanity.com/paper/2506.10929/) (2025)
- [Scalable Counterfactual Risk Estimation for Rare Events in Longitudinal Data](https://mlsanity.com/paper/2606.01539/) (2026)
- [Subdata Selection for Measurement-Constrained Linear Regression under Model Misspecification](https://mlsanity.com/paper/2610.19351/) (2026)

## Abstract (arXiv)

For classification problems with significant class imbalance, subsampling can reduce computational costs at the price of inflated variance in estimating model parameters. We propose a method for subsampling efficiently for logistic regression by adjusting the class balance locally in feature space via an accept-reject scheme. Our method generalizes standard case-control sampling, using a pilot estimate to preferentially select examples whose responses are conditionally rare given their features. The biased subsampling is corrected by a post-hoc analytic adjustment to the parameters. The method is simple and requires one parallelizable scan over the full data set. Standard case-control sampling is inconsistent under model misspecification for the population risk-minimizing coefficients θ^*. By contrast, our estimator is consistent for θ^* provided that the pilot estimate is. Moreover, under correct specification and with a consistent, independent pilot estimate, our estimator has exactly twice the asymptotic variance of the full-sample MLE - even if the selected subsample comprises a miniscule fraction of the full data set, as happens when the original data are severely imbalanced. The factor of two improves to 1+frac1c if we multiply the baseline acceptance probabilities by c>1 (and weight points with acceptance probability greater than 1), taking roughly frac1+c2 times as many data points into the subsample. Experiments on simulated and real data show that our method can substantially outperform standard case-control subsampling.