  Inherent bias within society can be amplified and perpetuated by artificial
intelligence (AI) systems. To address this issue, a wide range of solutions
have been proposed to identify and mitigate bias and enforce fairness for
individuals and groups. Recently, Graph Laplacian Regularizer (GLR), a
regularization technique from the semi-supervised learning literature has been
used as a substitute for the common Lipschitz condition to enhance individual
fairness. Notable prior work has shown that enforcing individual fairness
through a GLR can improve the transfer learning accuracy of AI models under
covariate shifts. However, the prior work defines a GLR on the source and
target data combined, implicitly assuming that the target data are available at
train time, which might not hold in practice. In this work, we investigated
whether defining a GLR independently on the train and target data could
maintain similar accuracy. Furthermore, we introduced the Normalized Fairness
Gain score (NFG) to measure individual fairness by measuring the amount of
gained fairness when a GLR is used versus not. We evaluated the new and
original methods under NFG, the Prediction Consistency (PC), and traditional
classification metrics on the German Credit Approval dataset. The results
showed that the two models achieved similar statistical mean performances over
five-fold cross-validation. Furthermore, the proposed metric showed that PC
scores can be misleading as the scores can be high and statistically similar to
fairness-enhanced models while NFG scores are small. This work therefore
provides new insights into when a GLR effectively enhances individual fairness
and the pitfalls of PC.
