Restoring balance: principled under/oversampling of data for optimal classification

TL;DR

This paper provides a theoretical framework for understanding how under- and oversampling strategies affect the generalization performance of linear classifiers in imbalanced data scenarios, supported by empirical validation.

Contribution

It derives analytical expressions for generalization curves in high-dimensional settings and predicts the impact of sampling strategies based on data statistics and class imbalance.

Findings

Mixed sampling strategies improve performance.

Theoretical predictions match empirical results.

Sampling effects depend on data moments and class imbalance.

Abstract

Class imbalance in real-world data poses a common bottleneck for machine learning tasks, since achieving good generalization on under-represented examples is often challenging. Mitigation strategies, such as under or oversampling the data depending on their abundances, are routinely proposed and tested empirically, but how they should adapt to the data statistics remains poorly understood. In this work, we determine exact analytical expressions of the generalization curves in the high-dimensional regime for linear classifiers (Support Vector Machines). We also provide a sharp prediction of the effects of under/oversampling strategies depending on class imbalance, first and second moments of the data, and the metrics of performance considered. We show that mixed strategies involving under and oversampling of data lead to performance improvement. Through numerical experiments, we show the relevance of our theoretical predictions on real datasets, on deeper architectures and with sampling strategies based on unsupervised probabilistic models.