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October 2014 Local case-control sampling: Efficient subsampling in imbalanced data sets
William Fithian, Trevor Hastie
Ann. Statist. 42(5): 1693-1724 (October 2014). DOI: 10.1214/14-AOS1220


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 $\theta^{*}$. By contrast, our estimator is consistent for $\theta^{*}$ 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 $1+\frac{1}{c}$ if we multiply the baseline acceptance probabilities by $c>1$ (and weight points with acceptance probability greater than 1), taking roughly $\frac{1+c}{2}$ 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.


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William Fithian. Trevor Hastie. "Local case-control sampling: Efficient subsampling in imbalanced data sets." Ann. Statist. 42 (5) 1693 - 1724, October 2014.


Published: October 2014
First available in Project Euclid: 11 September 2014

zbMATH: 1305.62096
MathSciNet: MR3257627
Digital Object Identifier: 10.1214/14-AOS1220

Primary: 62F10
Secondary: 62D05

Keywords: case-control sampling , logistic regression , subsampling

Rights: Copyright © 2014 Institute of Mathematical Statistics


Vol.42 • No. 5 • October 2014
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