A geometric framework for fairness

Fairness has emerged as a critical concern in the field of machine learning impacting its application in various domains. While there have been successful attempts to tackle fairness, many existing analyses rely on sophisticated mathematical methods that may lack intuitive understanding. Drawing inspiration from successful applications in other areas of machine learning, in this study, we propose a GEOmetric Framework for Fairness - GEOFFair - that represents distributions, ML models, fairness constraints, and hypothesis spaces as vectors and sets. The geometric framework aims to provide a more intuitive and rigorous understanding of fairness in Artificial Intelligence (AI). It enables visualizing mitigation techniques as movements in the vector space and aids in constructing proofs-by-witness by quickly identifying examples or counter-examples. Furthermore, the geometric framework offers a platform for studying various fairness properties, including geometrical distances between fairness vectors, relative fairness comparisons, and the exploration of symmetries, invariances, and trade-offs between fairness metrics.