Class Imbalance in Anomaly Detection: Learning from an Exactly Solvable Model

TL;DR

This paper introduces a theoretical framework based on an exactly solvable model to analyze class imbalance in anomaly detection, revealing nuanced effects of imbalance, noise, and data on learning performance.

Contribution

It provides the first theoretical analysis of class imbalance in anomaly detection using replica theory, offering insights into optimal imbalance levels and noise effects.

Findings

Optimal train imbalance differs from 50%, depending on data and noise.

Performance degrades rapidly with noise in high-noise regimes.

Conventional wisdom on class imbalance is challenged by the analysis.

Abstract

Class imbalance (CI) is a longstanding problem in machine learning, slowing down training and reducing performances. Although empirical remedies exist, it is often unclear which ones work best and when, due to the lack of an overarching theory. We address a common case of imbalance, that of anomaly (or outlier) detection. We provide a theoretical framework to analyze, interpret and address CI. It is based on an exact solution of the teacher-student perceptron model, through replica theory. Within this framework, one can distinguish several sources of CI: either intrinsic, train or test imbalance. Our analysis reveals that the optimal train imbalance is generally different from 50%, with a non trivial dependence on the intrinsic imbalance, the abundance of data and on the noise in the learning. Moreover, there is a crossover between a small noise training regime where results are independent of the noise level to a high noise regime where performances quickly degrade with noise. Our results challenge some of the conventional wisdom on CI and offer practical guidelines to address it.