Fair Representation: Guaranteeing Approximate Multiple Group Fairness for Unknown Tasks

Xudong Shen, Yongkang Wong, Mohan S. Kankanhalli

Abstract: Motivated by scenarios where data is used for diverse prediction tasks, we study whether fair representation can be used to guarantee fairness <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">for unknown tasks</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">for multiple fairness notions</i> . We consider seven group fairness notions that cover the concepts of independence, separation, and calibration. Against the backdrop of the fairness impossibility results, we explore approximate fairness. We prove that, although fair representation might not guarantee fairness for all prediction tasks, it does guarantee fairness for an important subset of tasks—the tasks for which the representation is discriminative. Specifically, all seven group fairness notions are linearly controlled by fairness and discriminativeness of the representation. When an incompatibility exists between different fairness notions, fair and discriminative representation hits the sweet spot that <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">approximately</i> satisfies all notions. Motivated by our theoretical findings, we propose to learn both fair and discriminative representations using pretext loss which self-supervises learning, and Maximum Mean Discrepancy as a fair regularizer. Experiments on tabular, image, and face datasets show that using the learned representation, downstream predictions <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">that we are unaware of when learning the representation</i> indeed become fairer. The fairness guarantees computed from our theoretical results are all valid.