Is There a Trade-Off Between Fairness and Accuracy? A Perspective Using Mismatched Hypothesis Testing

TL;DR

This paper challenges the common belief of an inherent fairness-accuracy trade-off in machine learning by using information theory to show that, under ideal conditions, both can be achieved simultaneously, and discusses implications for data bias.

Contribution

It introduces a novel perspective using mismatched hypothesis testing and Chernoff information to demonstrate the absence of a trade-off under ideal distributions, and explores how data bias affects this relationship.

Findings

Existence of ideal distributions where fairness and accuracy are simultaneously maximized

Trade-offs observed are due to biased datasets, not fundamental limitations

Active data collection can reduce fairness-accuracy trade-offs in practice

Abstract

A trade-off between accuracy and fairness is almost taken as a given in the existing literature on fairness in machine learning. Yet, it is not preordained that accuracy should decrease with increased fairness. Novel to this work, we examine fair classification through the lens of mismatched hypothesis testing: trying to find a classifier that distinguishes between two ideal distributions when given two mismatched distributions that are biased. Using Chernoff information, a tool in information theory, we theoretically demonstrate that, contrary to popular belief, there always exist ideal distributions such that optimal fairness and accuracy (with respect to the ideal distributions) are achieved simultaneously: there is no trade-off. Moreover, the same classifier yields the lack of a trade-off with respect to ideal distributions while yielding a trade-off when accuracy is measured with respect to the given (possibly biased) dataset. To complement our main result, we formulate an optimization to find ideal distributions and derive fundamental limits to explain why a trade-off exists on the given biased dataset. We also derive conditions under which active data collection can alleviate the fairness-accuracy trade-off in the real world. Our results lead us to contend that it is problematic to measure accuracy with respect to data that reflects bias, and instead, we should be considering accuracy with respect to ideal, unbiased data.