Review of Mathematical frameworks for Fairness in Machine Learning

TL;DR

This paper reviews mathematical fairness definitions in machine learning, analyzes their impact on algorithm performance, and introduces novel optimal fair classifiers and predictors under specific models.

Contribution

It provides a mathematical review of fairness criteria, explores their performance trade-offs, and derives new optimal classifiers and predictors for equality of odds.

Findings

Expressions for the optimal fair classifier and predictor under linear Gaussian models.

Analysis of the performance degradation due to fairness constraints.

Comparison of statistical parity and equality of odds criteria.

Abstract

A review of the main fairness definitions and fair learning methodologies proposed in the literature over the last years is presented from a mathematical point of view. Following our independence-based approach, we consider how to build fair algorithms and the consequences on the degradation of their performance compared to the possibly unfair case. This corresponds to the price for fairness given by the criteria $\textit{statistical parity}$ or $\textit{equality of odds}$. Novel results giving the expressions of the optimal fair classifier and the optimal fair predictor (under a linear regression gaussian model) in the sense of $\textit{equality of odds}$ are presented.