  Fairness in machine learning has attained significant focus due to the
widespread application in high-stake decision-making tasks. Unregulated machine
learning classifiers can exhibit bias towards certain demographic groups in
data, thus the quantification and mitigation of classifier bias is a central
concern in fairness in machine learning. In this paper, we aim to quantify the
influence of different features in a dataset on the bias of a classifier. To do
this, we introduce the Fairness Influence Function (FIF). This function breaks
down bias into its components among individual features and the intersection of
multiple features. The key idea is to represent existing group fairness metrics
as the difference of the scaled conditional variances in the classifier's
prediction and apply a decomposition of variance according to global
sensitivity analysis. To estimate FIFs, we instantiate an algorithm
FairXplainer that applies variance decomposition of classifier's prediction
following local regression. Experiments demonstrate that FairXplainer captures
FIFs of individual feature and intersectional features, provides a better
approximation of bias based on FIFs, demonstrates higher correlation of FIFs
with fairness interventions, and detects changes in bias due to fairness
affirmative/punitive actions in the classifier.
  The code is available at https://github.com/ReAILe/bias-explainer.
