Impossibility results for fair representation

Tosca Lechner, Nivasini Ananthakrishnan, Sushant Agarwal, Shai Ben-David

Keywords: Fairness, learning, data representation, theory, sample complexity

TL;DR: Showing that some common desiderata for fair data representation are provably unattainable.

Abstract: With the growing awareness to fairness in machine learning and the realization of the central role that data representation has in data processing tasks, there is an obvious interest in notions of fair data representations. We provide a formal framework for examining the fairness of data representations through the lens of their effect on decisions (mainly classification) made based on data represented that way. Using that framework, we prove that several desiderata for fair representations cannot be achieved. While some of our conclusions are intuitive, we formulate (and prove) crisp statements of such impossibilities, often contrasting impressions conveyed by many recent works on fair representations.

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