LOCAL CASE-CONTROL SAMPLING: EFFICIENT SUBSAMPLING IN IMBALANCED DATA SETS

doi:10.1214/14-AOS1220

2014-10-01

Fithian, William *

Trevor Hastie

DOI：10.1214/14-AOS1220

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摘要

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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 + 1/c we multiply the baseline acceptance probabilities by c > 1 (and weight points with acceptance probability greater than 1), taking roughly 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.

Keyword:

Logistic regression

case-control sampling

subsampling