Algorithmic Accountability in Small Data: Sample-Size-Induced Bias Within Classification Metrics

TL;DR

This paper reveals how combinatorics-induced sample-size bias affects classification metrics, especially in social applications with unequal group sizes, and proposes a model-agnostic correction method to improve fairness and trustworthiness.

Contribution

It uncovers the impact of combinatorics on sample-size bias in classification metrics and introduces a model-agnostic assessment and correction technique.

Findings

Sample-size bias significantly affects classification metrics in small or unequal groups.

Analysis of undefined cases in metrics can mislead evaluations.

Proposed correction improves fairness in classification assessments.

Abstract

Evaluating machine learning models is crucial not only for determining their technical accuracy but also for assessing their potential societal implications. While the potential for low-sample-size bias in algorithms is well known, we demonstrate the significance of sample-size bias induced by combinatorics in classification metrics. This revelation challenges the efficacy of these metrics in assessing bias with high resolution, especially when comparing groups of disparate sizes, which frequently arise in social applications. We provide analyses of the bias that appears in several commonly applied metrics and propose a model-agnostic assessment and correction technique. Additionally, we analyze counts of undefined cases in metric calculations, which can lead to misleading evaluations if improperly handled. This work illuminates the previously unrecognized challenge of combinatorics and probability in standard evaluation practices and thereby advances approaches for performing fair and trustworthy classification methods.