Principal Fairness: Removing Bias via Projections

TL;DR

This paper introduces a method using fair projections to reduce bias in data, enabling the recovery of fair, dense subgraphs and establishing complexity bounds for related approximation problems.

Contribution

It proposes a novel bias reduction technique via random projections in a fair subspace and applies it to the densest subgraph problem, providing theoretical and empirical results.

Findings

The method effectively recovers fair, dense subgraphs.

Approximation within a factor of 2 is NP-hard under the small set expansion hypothesis.

A polynomial-time algorithm with a matching approximation bound is presented.

Abstract

Reducing hidden bias in the data and ensuring fairness in algorithmic data analysis has recently received significant attention. We complement several recent papers in this line of research by introducing a general method to reduce bias in the data through random projections in a "fair" subspace. We apply this method to densest subgraph problem. For densest subgraph, our approach based on fair projections allows to recover both theoretically and empirically an almost optimal, fair, dense subgraph hidden in the input data. We also show that, under the small set expansion hypothesis, approximating this problem beyond a factor of 2 is NP-hard and we show a polynomial time algorithm with a matching approximation bound.