Optimal Downsampling for Imbalanced Classification with Generalized Linear Models

TL;DR

This paper develops an optimal downsampling method for imbalanced classification using generalized linear models, providing theoretical guarantees and demonstrating improved performance over existing methods through experiments.

Contribution

It introduces a pseudo maximum likelihood estimator for optimal downsampling in imbalanced classification with GLMs, with proven asymptotic properties and practical guidelines.

Findings

The estimator outperforms existing methods in experiments.

Optimal downsampling balances accuracy and efficiency.

Theoretical guarantees support the estimator's reliability.

Abstract

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.