Exploring the Linear Subspace Hypothesis in Gender Bias Mitigation

TL;DR

This paper investigates whether gender bias in word representations can be effectively isolated using linear methods, and introduces a nonlinear approach to test the linearity assumption, ultimately confirming the linear subspace hypothesis.

Contribution

It generalizes existing linear bias mitigation techniques to a nonlinear kernelized version and empirically verifies the linearity of gender bias in word embeddings.

Findings

Gender bias is well captured by a linear subspace.

The nonlinear method confirms the linearity assumption.

The approach improves bias mitigation techniques.

Abstract

Bolukbasi et al. (2016) presents one of the first gender bias mitigation techniques for word representations. Their method takes pre-trained word representations as input and attempts to isolate a linear subspace that captures most of the gender bias in the representations. As judged by an analogical evaluation task, their method virtually eliminates gender bias in the representations. However, an implicit and untested assumption of their method is that the bias subspace is actually linear. In this work, we generalize their method to a kernelized, nonlinear version. We take inspiration from kernel principal component analysis and derive a nonlinear bias isolation technique. We discuss and overcome some of the practical drawbacks of our method for non-linear gender bias mitigation in word representations and analyze empirically whether the bias subspace is actually linear. Our analysis shows that gender bias is in fact well captured by a linear subspace, justifying the assumption of Bolukbasi et al. (2016).