Parity-based cumulative fairness-aware boosting

Abstract

Data-driven AI systems can lead to discrimination on the basis of protected attributes like gender or race. One cause for this is the encoded societal biases in the training data (e.g., under-representation of females in the tech workforce), which is aggravated in the presence of unbalanced class distributions (e.g., when “hired” is the minority class in a hiring application). State-of-the-art fairness-aware machine learning approaches focus on preserving the overall classification accuracy while mitigating discrimination. In the presence of class-imbalance, such methods may further aggravate the problem of discrimination by denying an already underrepresented group (e.g., females) the fundamental rights of equal social privileges (e.g., equal access to employment). To this end, we propose AdaFair, a fairness-aware boosting ensemble that changes the data distribution at each round, taking into account not only the class errors but also the fairness-related performance of the model defined cumulatively based on the partial ensemble. Except for the in-training boosting of the group discriminated over each round, AdaFair directly tackles imbalance during the post-training phase by optimizing the number of ensemble learners for balanced error performance. AdaFair can facilitate different parity-based fairness notions and mitigate effectively discriminatory outcomes.

Appendix

1.1 Cumulative versus non-cumulative fairness

Statistical Parity In Fig. 8, we show the comparison of AdaFair versus AdaFair NoCumul w.r.t statistical parity for each dataset. As we see, AdaFair NoCumul produces higher discriminatory outcomes than AdaFair on all datasets. For the Adult census dataset, we observe a 31%$\uparrow$ increase, 12%$\uparrow$ increase for the Bank dataset, 15%$\uparrow$ for the Compass and 15%$\uparrow$ for the KDD census dataset. The cumulative notion of fairness allows AdaFair to effectively mitigate the discriminatory outcomes in contrast to the non-cumulative version.

In Fig. 9, we compare the per round $\delta SP$ of AdaFair NoCumul and AdaFair. $\delta SP$ refers to the fairness-related cost (u) that is assigned to instances based on the discriminatory behavior of the model (Eq. (9)). We observe that AdaFair NoCumul produces fairness-related costs, which highly fluctuate, in contrast to AdaFair, in all the datasets. The non-cumulative version cannot stabilize the fairness-related costs since it depends on the behavior of individual weak learns rather than the cumulative behavior of the model.

Fig. 9

Statistical parity, fairness-related costs per boosting round: AdaFair versus AdaFair NoCumul

Equal Opportunity In Fig. 10, we show the comparison of AdaFair versus AdaFair NoCumul w.r.t equal opportunity for each dataset. Same as in the statistical parity case, AdaFair NoCumul produces more discriminatory outcomes in contrast to AdaFair. For the Adult census dataset, there is a 15%$\uparrow$ increase, 2%$\uparrow$ increase for the Bank dataset, 12%$\uparrow$ increase for the Compass, and 8%$\uparrow$ increase for the KDD census dataset.

Similar behavior to statistical parity is also observed in Fig. 11, where we report $\delta \text {FNR}$ values for the cumulative and non-cumulative approaches; $\delta \text {FNR}$ values are employed as fairness-related costs and are derived from Eq. (11). The non-cumulative version is unstable and produces highly fluctuating fairness-related costs in contrast to AdaFair in all datasets.

Fig. 10

Equal opportunity: AdaFair versus AdaFair NoCumul

Fig. 11

Equal opportunity, fairness-related costs per boosting round: AdaFair versus AdaFair NoCumul

Fig. 12

Statistical parity: impact of parameter c

1.2 The effect of balanced error

We show the impact of parameter c for all the employed fairness notions in Figs. 12 and 13.

Statistical Parity In Fig. 12, we show the impact of parameter c in case of statistical parity. As we observe, all the imbalanced datasets show the worst performance in terms of balanced accuracy when $c=0$; however, statistical parity is close to 0. As the parameter c increases, the balanced accuracy increases and the statistical parity remains close to 0. However, in the case of statistical parity, we observe that the balanced accuracy is not affected significantly in contrast to the other two fairness notions. Such behavior is caused due to the fairness’ notion, which forces parity between protected and non-protected groups on the predicted outcomes; thus, statistical parity can force AdaFair to predict more instances in the positive class indirectly.

Equal Opportunity In Fig. 13, we show the impact of c when AdaFair tunes for equal opportunity. Similar to disparate mistreatment, AdaFair can maintain its low discrimination values w.r.t equal opportunity and at the same time increase the balanced accuracy as the parameter c increases. For example, AdaFair’s balanced accuracy increases 8% for $c=0$ to $c=1$ and at the same time equal opportunity is close to 0. This behavior is similar for all the employed imbalanced datasets. For the Compass dataset, the parameter c does not affect the performance significantly since the dataset is class balanced.

Fig. 13

Equal opportunity: impact of parameter c