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Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment
Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rodriguez, Krishna P. Gummadi
TL;DR
Automated classifiers can misclassify social groups at different rates even when trained to minimize overall error, creating an unfairness the paper calls disparate mistreatment. The paper formalizes this notion, embeds corresponding measures as convex-concave constraints for decision-boundary classifiers, and evaluates the approach on synthetic and real-world data. The experiments report effective reduction of disparate mistreatment, often with a small accuracy cost, while identifying limitations for small datasets and some error-rate formulations.
Problem
Classifiers trained on historical decisions can produce different misclassification rates across sensitive groups, but existing fairness notions are less suitable when ground truth for those decisions is available.
Method
The paper defines disparate mistreatment through group error rates and incorporates its measures into convex-concave constraints for decision-boundary-based classifiers.
Results
The methodology effectively avoids disparate mistreatment on synthetic and real-world datasets, often at a small accuracy cost; methods achieve similar accuracy at a given fairness level on COMPAS.
Takeaways & Limitations
Fairness can be expressed as a flexible trade-off between disparate-mistreatment control and accuracy, with simultaneous avoidance of disparate treatment also supported.
Takeaways & Limitations
The method covers overall, false-positive, and false-negative rates, while false-discovery and false-omission constraints remain computationally challenging; small datasets can also yield incomplete fairness removal.
Abstract
from arXiv · showhide
Automated data-driven decision making systems are increasingly being used to assist, or even replace humans in many settings. These systems function by learning from historical decisions, often taken by humans. In order to maximize the utility of these systems (or, classifiers), their training involves minimizing the errors (or, misclassifications) over the given historical data. However, it is quite possible that the optimally trained classifier makes decisions for people belonging to different social groups with different misclassification rates (e.g., misclassification rates for females are higher than for males), thereby placing these groups at an unfair disadvantage. To account for and avoid such unfairness, in this paper, we introduce a new notion of unfairness, disparate mistreatment, which is defined in terms of misclassification rates. We then propose intuitive measures of disparate mistreatment for decision boundary-based classifiers, which can be easily incorporated into their formulation as convex-concave constraints. Experiments on synthetic as well as real world datasets show that our methodology is effective at avoiding disparate mistreatment, often at a small cost in terms of accuracy.
1. INTRODUCTION
The paper introduces disparate mistreatment, an unfairness notion based on unequal misclassification rates across sensitive groups, for settings where decision ground truth is available. It proposes classifier constraints to reduce this unfairness while preserving accuracy trade-offs.
- Disparate treatment changes decisions with sensitive attributes, whereas disparate impact concerns disproportionate benefits or harms across sensitive groups.
- Disparate mistreatment occurs when groups with different sensitive-attribute values have different misclassification rates.The paper targets scenarios where ground truth for historical decisions is available.
- The paper considers overall errors and application-specific rates such as false positives, false negatives, false discoveries, and false omissions.The relevant rate depends on the application and the cost of each misclassification.
- The proposed measures for decision-boundary classifiers become convex-concave constraints that can be solved efficiently using convex-concave programming.
- Experiments on synthetic and real-world datasets show that the methodology can avoid disparate mistreatment, often with a small accuracy cost.
2. BACKGROUND AND RELATED WORK
The paper distinguishes disparate mistreatment from disparate treatment and disparate impact, emphasizing that ground truth determines which fairness notion is informative. It motivates disparate mistreatment for validated decisions while reviewing related detection, mitigation, and thresholding approaches.
- Disparate mistreatment concerns unequal decision errors, while disparate treatment concerns different outputs for otherwise similar people differing in sensitive attributes.
- Disparate impact concerns groups receiving beneficial or harmful outcomes at different frequencies, independently of whether decisions are correct.
- Disparate impact remains appealing when ground truth is unavailable and historical decisions cannot be trusted, such as potentially biased recruiting or loan decisions.
- When decision correctness is reliably known, disparate impact can treat justified outcome differences as unfair and risk reverse discrimination.
- Prior work has studied detecting and removing treatment- and impact-based unfairness, while related work also uses ground truth or group-specific post-processing thresholds.
3. FORMALIZING NOTIONS OF FAIRNESS
The paper formalizes fairness notions for binary decision-boundary classifiers using sensitive features and probability constraints. Disparate mistreatment is defined through equal error rates, with multiple rate definitions reflecting different application priorities.
- A binary classifier learns a decision boundary minimizing loss over labeled feature vectors and predicts from the signed distance to that boundary.The sensitive feature is assumed binary for exposition but can be generalized to categorical or multiple sensitive features.
- Absence of disparate treatment requires the prediction distribution given features to remain unchanged after observing the sensitive feature.
- Absence of disparate impact requires equal positive-prediction probabilities across sensitive-feature groups.
- Absence of disparate mistreatment requires equal misclassification rates across groups, measured using overall error, false-positive, false-negative, false-discovery, or false-omission rates.
- The paper focuses its elimination method on overall, false-positive, and false-negative rates, leaving false-discovery and false-omission constraints for future work because of computational complexity.
MISTREATMENT
The paper replaces difficult disparate-mistreatment constraints with a covariance-based proxy and incorporates it into tractable convex-concave training formulations. The resulting approach supports decision-boundary classifiers while allowing simultaneous removal of disparate treatment when sensitive attributes are excluded from decision-time features.
- Classifier training: A fair logistic regressor minimizes its training loss subject to upper and lower bounds on the difference between group misclassification rates.The constrained formulation selects an optimal decision boundary from the space of boundaries satisfying the specified fairness tolerance.
- Optimization: The proxy constraints are generally non-convex, but rewriting them using convex gθ yields a difference-of-convex formulation.For binary sensitive attributes, the relevant sums can be split by z=0 and z=1; applying both false-positive and false-negative constraints is also possible.
- Proxy for disparate mistreatment: The method measures disparate mistreatment through covariance between sensitive attributes and signed distances to the decision boundary for misclassified users.The covariance proxy is close to zero when the corresponding group misclassification conditions are satisfied.
- Proxy for disparate mistreatment: The covariance threshold c controls how closely the learned decision boundary adheres to the disparate-mistreatment requirement.Smaller fairness tolerances impose stricter adherence to the constraint.
- Optimization: The resulting problem is a Disciplined Convex-Concave Program for any convex loss and can be solved using convex-concave programming heuristics.The formulation applies to a wide variety of linear and nonlinear decision-boundary classifiers, including logistic regression and SVMs.
- Classifier training: Keeping feature vector x disjoint from sensitive attribute z allows the formulation to remove disparate mistreatment and disparate treatment simultaneously.The method therefore does not require sensitive-attribute information at decision time.
5. EVALUATION
Experiments on synthetic and COMPAS data evaluate fairness constraints for logistic regression, measuring disparate mistreatment through false positive and false negative rates. The method generally reduces group-wise misclassification disparities, with accuracy costs that depend on the fairness target, data distribution, and method.
- Experimental setup: Five random 50%-train/50%-test splits evaluate logistic regression using average accuracy and fairness statistics.The evaluation focuses on false positive and false negative rates as disparate-mistreatment measures.
- Metrics: DF_PR and DF_NR quantify group differences in false positive and false negative rates, with values nearer 0 indicating less disparate mistreatment.The measures compare conditional misclassification probabilities across sensitive-attribute groups.
- Synthetic data: 0.85 accuracy accompanied DF_NR = 0 and DF_PR = 0.19 for the unconstrained synthetic classifier, demonstrating false-positive disparity.The classifier was trained on distributions that differed across sensitive-attribute groups.
- Synthetic data: As the fairness constraint c approaches zero, group false positive rates converge and DF_PR approaches 0, while accuracy decreases.DF_NR remains close to zero in this synthetic scenario, although its invariance depends on the data distribution.
- Synthetic data: When DF_PR and DF_NR have opposite signs, controlling one error rate can also reduce the other; when they share a sign, controlling one can exacerbate the other.Simultaneously controlling both rates can produce similar results in the first setting but a larger accuracy drop in the second.
- Performance comparison: Using sensitive features, Our methodsen matched Hardt et al.'s performance; removing both disparate mistreatment and disparate treatment incurred only about a 5% further accuracy drop.The comparison concerns synthetic datasets and contrasts methods that use sensitive information with the proposed simultaneous-removal scheme.
- ProPublica COMPAS: The COMPAS logistic classifier achieved 0.668 accuracy, with black-versus-white false positive rates of 0.35 and 0.17 and false negative rates of 0.31 and 0.61.These disparities correspond to DF_PR = 0.18 and DF_NR = −0.30.
- ProPublica COMPAS: On COMPAS, all three methods achieved similar accuracy for a given fairness level, while controlling one error rate also reduced disparity in the other.The method significantly reduced disparate mistreatment at a modest accuracy cost, but did not achieve zero disparity in every case.
6. DISCUSSION AND FUTURE WORK
The method supports a tunable tradeoff between disparate-mistreatment fairness and accuracy, while also enabling simultaneous avoidance of disparate mistreatment and disparate treatment. The paper identifies computational and estimation limitations and proposes extending the formulation to additional error-rate measures.
- The method provides a flexible tradeoff between disparate-mistreatment fairness and accuracy.
- It can avoid disparate mistreatment and disparate treatment simultaneously, including when sensitive-attribute information is unavailable or prohibited.
- The current formulation covers false positive and false negative rates, while incorporating false discovery and false omission rates remains computationally non-trivial.
- Training uses a disciplined convex-concave program solved with heuristic methods, which do not guarantee global optimality.
- Monte Carlo covariance approximations may be inaccurate on smaller datasets, although they are expected to work well with reasonable training data.