Fair Regression: Quantitative Definitions and Reduction-based Algorithms (1905.12843v1)

Abstract: In this paper, we study the prediction of a real-valued target, such as a risk score or recidivism rate, while guaranteeing a quantitative notion of fairness with respect to a protected attribute such as gender or race. We call this class of problems \emph{fair regression}. We propose general schemes for fair regression under two notions of fairness: (1) statistical parity, which asks that the prediction be statistically independent of the protected attribute, and (2) bounded group loss, which asks that the prediction error restricted to any protected group remain below some pre-determined level. While we only study these two notions of fairness, our schemes are applicable to arbitrary Lipschitz-continuous losses, and so they encompass least-squares regression, logistic regression, quantile regression, and many other tasks. Our schemes only require access to standard risk minimization algorithms (such as standard classification or least-squares regression) while providing theoretical guarantees on the optimality and fairness of the obtained solutions. In addition to analyzing theoretical properties of our schemes, we empirically demonstrate their ability to uncover fairness--accuracy frontiers on several standard datasets.

Fair Regression: Quantitative Definitions and Reduction-based Algorithms

The paper on "Fair Regression: Quantitative Definitions and Reduction-based Algorithms" introduces a comprehensive framework aimed at addressing fairness in regression tasks. Traditional approaches in the field of machine learning focus extensively on fair classification; however, the paper acknowledges a critical need to extend fairness considerations to regression contexts where predictions are continuous. This paper proposes algorithms designed to ensure fairness in regression predictions relative to protected attributes such as race and gender.

Core Contributions

The authors articulate two primary definitions of fairness tailored for regression:

1. Statistical Parity (SP): This requires that the prediction is statistically independent of the protected attribute. In essence, the distribution of predictions should be identical across various subgroups identified by the protected attribute.
2. Bounded Group Loss (BGL): Under this criterion, the authors demand that the prediction error, restricted to any protected group, should remain below a predetermined threshold for fairness. This ensures that all subgroups experience prediction errors that are within an acceptable range, preventing scenarios where less representative groups suffer from disproportionately high errors.

While the paper narrows its focus to SP and BGL, the proposed methods are versatile enough to be applied across tasks involving Lipschitz-continuous loss functions, covering a broad spectrum of commonly used regression models, including but not limited to least-squares and logistic regression.

Methodological Insights

The authors introduce reduction-based algorithms that transform the problem of fair regression into one that can be tackled with existing machine learning paradigms:

• For SP, the regression task with fairness constraints is reformulated using a cost-sensitive classification framework. The problem is then addressed with a series of reductions that facilitate the use of standard classification tools, thus simplifying the complex task of ensuring fairness in predictive distributions.
• For BGL, the algorithm reduces the regression problem into a weighted risk minimization task. This reduction leverages existing regression techniques adapted to accommodate fairness constraints, ensuring balanced outcomes across all protected groups.

Through extensive theoretical analysis, the paper provides guarantees on both the fairness of predictions and the computational feasibility of the proposed methods. The significant theoretical contribution lies in the algorithmic reductions, which ensure that the transformation into cost-sensitive classification or weighted regression retains essential fairness properties.

Empirical Evaluation

Empirically, the paper demonstrates the effectiveness of the proposed algorithms on standard datasets, thereby uncovering the "fairness-accuracy frontier" — the trade-off between ensuring fairness and maintaining predictive accuracy. By analyzing the performance of the algorithms, the paper shows that it is indeed possible to manage fairness constraints without excessively sacrificing accuracy.

Implications and Future Directions

This research has profound implications in any domain where decisions based on regression predictions could perpetuate or exacerbate inequality. By systematically introducing and proving the feasibility of fair regression, the authors provide a critical tool for technologists and policymakers intent on developing equitable ML solutions.

The versatility of the reduction-based approach invites future exploration into more sophisticated definitions of fairness. Moreover, as AI continues to integrate into diverse aspects of society, the need to continuously evaluate and evolve our mechanisms for enforcing fairness in predictive models becomes paramount.

Overall, this paper makes a substantial contribution to the literature on fairness in machine learning by extending these considerations from classification into the critical, yet often overlooked, domain of regression. The promise of these methodologies could lead to tangible improvements in the fairness of AI-driven decision systems across various applications.