Review of Mathematical frameworks for Fairness in Machine Learning
This work addresses fairness in ML for researchers and practitioners, but it is incremental as it builds on existing frameworks with new theoretical results.
The paper reviews mathematical fairness definitions and methodologies in machine learning, focusing on the trade-off between fairness and performance, and presents novel optimal fair classifier and predictor expressions under equality of odds in a linear regression Gaussian model.
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.