# Fair Representation: Guaranteeing Approximate Multiple Group Fairness for Unknown Tasks

**Authors:** Xudong Shen, Yongkang Wong, Mohan Kankanhalli  
**arXiv:** [2109.00545](https://arxiv.org/abs/2109.00545)  
**Date:** 2021-09-01  
**Summary page:** https://www.summarizepaper.com/en/paper/2109.00545v2/

## Key points

- Fair representation can guarantee fairness for unknown prediction tasks and multiple fairness notions simultaneously.
- Seven group fairness notions are considered, covering independence, separation, and calibration concepts.
- Approximate fairness is explored and fair representation is proven to guarantee fairness for a subset of tasks where the representation is discriminative.
- All seven group fairness notions are linearly controlled by the representation's fairness and discriminativeness.
- When incompatibility exists between different notions, fair and discriminative representation satisfies all approximately.
- Pretext loss is proposed to self-supervise learning important semantics, while Maximum Mean Discrepancy serves as a fair regularizer in a constrained optimization problem solved using a two-player game approach to learn both fair and discriminative representations.
- Experiments on tabular, image, and face datasets show downstream predictions become fairer for all seven group fairness notions using the learned representation.
- Theoretical findings provide valid fairness guarantees for these experiments.

## Summary

This paper explores the use of fair representation to guarantee fairness for unknown prediction tasks and multiple fairness notions simultaneously. The authors consider seven group fairness notions that cover independence, separation, and calibration concepts. Despite the backdrop of fairness impossibility results, they explore approximate fairness and prove that fair representation guarantees fairness for a subset of tasks where the representation is discriminative. All seven group fairness notions are linearly controlled by the representation's fairness and discriminativeness. When an incompatibility exists between different notions, fair and discriminative representation satisfies all approximately. To learn both fair and discriminative representations, they propose using pretext loss to self-supervise learning important semantics and Maximum Mean Discrepancy as a fair regularizer in a constrained optimization problem solved using a two-player game approach. Experiments on tabular, image, and face datasets show downstream predictions become fairer for all seven group fairness notions using the learned representation. The authors' theoretical findings provide valid fairness guarantees for these experiments. Overall, this work provides insights into how to achieve approximate multiple group fairness in unknown prediction tasks with fair representations while addressing incompatibilities between different notions of group fairness.