Fairness of Deep Ensembles: On the interplay between per-group task difficulty and under-representation

TL;DR

The paper investigates whether simple homogeneous ensembles can reduce fairness gaps across protected attributes without sacrificing overall performance. It uses synthetic and real datasets (CelebA and CheXpert) to study how per-group representation interacts with subgroup task difficulty, showing positive-sum fairness where both groups gain and the overall accuracy improves. It demonstrates that the optimal training balance shifts away from 50-50 when subgroup difficulty differs, sometimes favoring over-representation of the harder group, and that this principle applies in real-world tasks as well. The results suggest ensembles are a practical fairness tool and highlight the need for intersectional, difficulty-aware data balancing in fairness research.

Abstract

Ensembling is commonly regarded as an effective way to improve the general performance of models in machine learning, while also increasing the robustness of predictions. When it comes to algorithmic fairness, heterogeneous ensembles, composed of multiple model types, have been employed to mitigate biases in terms of demographic attributes such as sex, age or ethnicity. Moreover, recent work has shown how in multi-class problems even simple homogeneous ensembles may favor performance of the worst-performing target classes. While homogeneous ensembles are simpler to implement in practice, it is not yet clear whether their benefits translate to groups defined not in terms of their target class, but in terms of demographic or protected attributes, hence improving fairness. In this work we show how this simple and straightforward method is indeed able to mitigate disparities, particularly benefiting under-performing subgroups. Interestingly, this can be achieved without sacrificing overall performance, which is a common trade-off observed in bias mitigation strategies. Moreover, we analyzed the interplay between two factors which may result in biases: sub-group under-representation and the inherent difficulty of the task for each group. These results revealed that, contrary to popular assumptions, having balanced datasets may be suboptimal if the task difficulty varies between subgroups. Indeed, we found that a perfectly balanced dataset may hurt both the overall performance and the gap between groups. This highlights the importance of considering the interaction between multiple forces at play in fairness.

Figures (6)

• Figure 1: Impact of ensembling on an imbalanced scenario (20% male and 80% female) and with a label noise applied to 40% of female samples before training the models. Ensembles help to improve the performance of both subgroups, translating into an improvement of the overall performance. The relative improvements tend to be greater for the underperforming one (male in this scenario), reducing the gap between the groups.
• Figure 2: Results for the label noise synthetic scenario. Each column represents different noise levels in the female subgroup while keeping a constant 20% under-representation of males (20-80 M-F). (a) Samples of both distributions under different noise-balance configurations. The following rows correspond to (b) model accuracy for male (orange), female (light blue), and overall (green); (c) absolute performance gap (line color represents the group that is being benefited), and (d) relative improvements by the ensemble size. Dashed lines correspond to the same noise configuration but in a balanced scenario (50-50 M-F).
• Figure 3: Results for the label noise synthetic scenario. (Left) Overall accuracy and gap for different noise levels by the balance ratio between male and female subgroups for label noise scenario. (Right) Ideal male-female balance ratio for the different noise percentages. As the discrepancy in difficulty increases for both subgroups, more samples are needed for the most difficult one to achieve the best overall performance and minimum gap between the groups.
• Figure 4: (Top) For CheXpert, female was identified as the most difficult group, and we found an ideal balance ratio of 40-60 M-F (more females during training) achieving positive-sum fairness. (Bottom) For CelebA, the male subgroup was the most difficult one, and the ideal balanced ratio was 80-20 M-F (more males during training).
• Figure 5: Results for the rotating decision boundary synthetic scenario. Each column represents a different angle on which the decision boundary is rotated for the female subgroup. The higher the angle, the higher the difficulty for this subgroup. Every case was trained with a sub-representation of males by 40% (40-60 M-F). (a) Samples of both distributions under different angle-balance configurations (in green, the decision boundary with its corresponding angle). The following rows correspond to (b) model accuracy for male (orange), female (light blue), and overall (green); (c) absolute performance gap (line color represents the group that is being benefited), and (d) relative improvements by the ensemble size. Dashed lines correspond to the same angle configuration but in a balanced scenario (50-50 M-F).