Fairness Uncertainty Quantification: How certain are you that the model is fair?

TL;DR

This paper develops a method to quantify the uncertainty in fairness metrics of models trained with stochastic gradient descent, providing confidence intervals for fairness measures like Disparate Impact and Disparate Mistreatment.

Contribution

It introduces a novel approach to construct confidence intervals for fairness in online SGD-trained classifiers, extending bootstrap methods to constrained optimization.

Findings

Asymptotic normality of fairness measures established

Online bootstrap method effectively estimates covariance for CI construction

Method validated on synthetic and real datasets

Abstract

Fairness-aware machine learning has garnered significant attention in recent years because of extensive use of machine learning in sensitive applications like judiciary systems. Various heuristics, and optimization frameworks have been proposed to enforce fairness in classification \cite{del2020review} where the later approaches either provides empirical results or provides fairness guarantee for the exact minimizer of the objective function \cite{celis2019classification}. In modern machine learning, Stochastic Gradient Descent (SGD) type algorithms are almost always used as training algorithms implying that the learned model, and consequently, its fairness properties are random. Hence, especially for crucial applications, it is imperative to construct Confidence Interval (CI) for the fairness of the learned model. In this work we provide CI for test unfairness when a group-fairness-aware, specifically, Disparate Impact (DI), and Disparate Mistreatment (DM) aware linear binary classifier is trained using online SGD-type algorithms. We show that asymptotically a Central Limit Theorem holds for the estimated model parameter of both DI and DM-aware models. We provide online multiplier bootstrap method to estimate the asymptotic covariance to construct online CI. To do so, we extend the known theoretical guarantees shown on the consistency of the online bootstrap method for unconstrained SGD to constrained optimization which could be of independent interest. We illustrate our results on synthetic and real datasets.