Understanding the Limitations of Fairness Surrogate Functions and Proposing Improved Approaches for Algorithmic Fairness

Core Concepts

Fairness surrogate functions used in algorithmic fairness may exhibit a significant gap between the fairness definition and the surrogate, leading to unfair outcomes. Additionally, the use of unbounded surrogate functions can result in high instability. This paper proposes solutions, including a general sigmoid surrogate and a balanced surrogate approach, to address these issues and provide fairness and stability guarantees.

Abstract

The paper focuses on understanding the limitations of fairness surrogate functions and proposing improved approaches to address them. Key highlights: The authors demonstrate the importance of the "surrogate-fairness gap", which is the disparity between the fairness definition and the fairness surrogate function. This gap can lead to unfair outcomes even when the fairness constraint is satisfied. The authors also highlight the issue of high variance with unbounded surrogate functions, which can result in unstable fairness guidance for the classifier. The authors identify the "large margin points" issue, where data points significantly distant from the decision boundary can amplify the surrogate-fairness gap and instability. To address these challenges, the authors propose a general sigmoid surrogate function that simultaneously reduces the surrogate-fairness gap and the variance, providing fairness and stability guarantees. The authors also introduce a novel "balanced surrogate" approach that iteratively reduces the surrogate-fairness gap to improve fairness. Experiments on three real-world datasets demonstrate that the proposed methods consistently improve fairness and stability while maintaining comparable accuracy to the baselines.

Stats

"There is a surrogate-fairness gap between \DDP_S and ^DDP_S(ϕ)." (Proposition 1) "If we choose unbounded surrogate function (such as ϕ(x) = x ∈[-∞, +∞] for the original CP), the resulting values of ϕ(x) are not constrained within the range [0, 1]. Therefore, we cannot conclude that ^DDP_S(ϕ) ∈[-1, 1]. Consequently, we also cannot conclude that Var[^DDP_S(ϕ)] ∈[0, 1]." (Section 4.1) "Over 5% points are large margin points for Adult and COMPAS." (Section 4.2)

Quotes

"There is a surrogate-fairness gap between \DDP_S and ^DDP_S(ϕ)." (Proposition 1) "If we choose unbounded surrogate function (such as ϕ(x) = x ∈[-∞, +∞] for the original CP), the resulting values of ϕ(x) are not constrained within the range [0, 1]. Therefore, we cannot conclude that ^DDP_S(ϕ) ∈[-1, 1]. Consequently, we also cannot conclude that Var[^DDP_S(ϕ)] ∈[0, 1]." (Section 4.1) "Over 5% points are large margin points for Adult and COMPAS." (Section 4.2)

Key Insights Distilled From

Understanding Fairness Surrogate Functions in Algorithmic Fairness

by Wei Yao,Zhan... at arxiv.org 04-10-2024

https://arxiv.org/pdf/2310.11211.pdf

Deeper Inquiries

How can we automatically search for a suitable parameter w in the general sigmoid surrogate function to achieve improved fairness performance while reducing variance?

To automatically search for a suitable parameter w in the general sigmoid surrogate function, we can employ optimization techniques such as grid search, random search, or more advanced methods like Bayesian optimization or genetic algorithms. Grid Search: In grid search, we define a grid of hyperparameters (in this case, different values of w) and evaluate the model performance for each combination. We select the parameter w that gives the best fairness performance while reducing variance. Random Search: Random search involves randomly sampling hyperparameters from a predefined range. By evaluating the model with different values of w, we can identify the parameter that optimizes fairness and stability. Bayesian Optimization: Bayesian optimization is a sequential model-based optimization technique that uses probabilistic models to predict the performance of different hyperparameter configurations. It balances exploration and exploitation to efficiently search for the optimal w. Genetic Algorithms: Genetic algorithms mimic the process of natural selection to search for the best hyperparameters. By encoding the parameter w as genes in a population, evolving solutions through selection, crossover, and mutation can help find the optimal w for improved fairness and reduced variance. By iteratively evaluating the model with different values of w and updating the parameter based on the performance metrics, we can automate the search for the suitable parameter in the general sigmoid surrogate function.

What other techniques, beyond the balanced surrogate method, can be used to further reduce the surrogate-fairness gap and improve the fairness of unbounded surrogate functions?

In addition to the balanced surrogate method, several techniques can be employed to further reduce the surrogate-fairness gap and enhance the fairness of unbounded surrogate functions: Regularization: Introducing regularization terms in the optimization objective that penalize unfair predictions can help constrain the model to produce fair outcomes. Fairness regularization can be tailored to specific fairness definitions to reduce the gap. Ensemble Methods: Combining multiple models trained with different surrogate functions can help mitigate the shortcomings of individual surrogates. By aggregating predictions from diverse models, ensemble methods can improve fairness and stability. Fair Data Augmentation: Augmenting the dataset with synthetic samples generated using techniques like SMOTE (Synthetic Minority Over-sampling Technique) can balance the distribution of sensitive attributes. By creating a more balanced dataset, the surrogate-fairness gap can be reduced. Adversarial Training: Adversarial training involves training the model against an adversary that tries to maximize the unfairness. By iteratively optimizing the model to minimize the unfairness while the adversary maximizes it, the model can learn to produce fair predictions. Fair Representation Learning: Learning fair representations of the data by disentangling sensitive attributes from other features can help in reducing bias. By ensuring that the model focuses on relevant features rather than sensitive attributes, fairness can be improved. By combining these techniques with the balanced surrogate method, we can further enhance the fairness of unbounded surrogate functions and reduce the surrogate-fairness gap.

Can the insights gained from this study on fairness surrogate functions be extended to other fairness definitions beyond demographic parity?

Yes, the insights gained from the study on fairness surrogate functions, such as the importance of the surrogate-fairness gap, stability considerations, and the impact of large margin points, can be extended to other fairness definitions beyond demographic parity. Equal Opportunity: The concept of the surrogate-fairness gap and the need to reduce it to achieve fairness can be applied to the Equal Opportunity metric, which focuses on ensuring equal true positive rates across different groups. Predictive Parity: Insights on reducing variance and addressing large margin points can be relevant to Predictive Parity, which aims to achieve equal positive predictive values for different groups. Individual Fairness: Techniques to improve fairness and reduce the surrogate-fairness gap can also be extended to Individual Fairness, which requires similar individuals to be treated similarly. By adapting the methodologies and considerations from this study to other fairness definitions, researchers can enhance the fairness of machine learning models across a broader range of applications and contexts.