Towards a Fairer Non-negative Matrix Factorization

TL;DR

This paper proposes a modified non-negative matrix factorization method using a min-max objective to improve fairness across groups, with practical algorithms and experiments demonstrating its potential benefits and trade-offs.

Contribution

It introduces a fairness-aware modification to NMF via a min-max objective, along with algorithms and experimental validation for bias mitigation.

Findings

The method can improve group fairness in NMF applications.

Fairness improvements may sometimes increase individual error.

Fairness is context-dependent and requires careful method choice.

Abstract

There has been a recent critical need to study fairness and bias in machine learning (ML) algorithms. Since there is clearly no one-size-fits-all solution to fairness, ML methods should be developed alongside bias mitigation strategies that are practical and approachable to the practitioner. Motivated by recent work on ``fair" PCA, here we consider the more challenging method of non-negative matrix factorization (NMF) as both a showcasing example and a method that is important in its own right for both topic modeling tasks and feature extraction for other ML tasks. We demonstrate that a modification of the objective function, by using a min-max formulation, may \textit{sometimes} be able to offer an improvement in fairness for groups in the population. We derive two methods for the objective minimization, a multiplicative update rule as well as an alternating minimization scheme, and discuss implementation practicalities. We include a suite of synthetic and real experiments that show how the method may improve fairness while also highlighting the important fact that this may sometime increase error for some individuals and fairness is not a rigid definition and method choice should strongly depend on the application at hand.