# Fairer non-negative matrix factorization

## TL;DR

This paper introduces a fairer version of non-negative matrix factorization to reduce bias in machine learning, while acknowledging trade-offs in accuracy and fairness definitions.

## Contribution

The novel contribution is a min-max formulation for fair NMF with practical algorithms and experiments showing fairness improvements.

## Key findings

- A min-max objective modification can improve fairness in NMF for certain groups.
- Two practical optimization methods are derived: multiplicative updates and alternating minimization.
- Fairness improvements may increase error for some individuals, highlighting the need for application-specific choices.

## 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 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.