Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment

1. INTRODUCTION

• When ground truth is available, it can explain group differences in beneficial outcomes, making disparate impact unsuitable for assessing unfairness in those scenarios.Prior approaches addressed settings with biased historical decisions but no ground truth for judging their correctness.Source: §1 · p. 1
• Disparate mistreatment occurs when misclassification rates differ across groups defined by a sensitive attribute, such as race.The introduction contrasts it with disparate treatment, where decisions change with sensitive-attribute information, and disparate impact, where outcomes disproportionately benefit or hurt groups.Source: §1 · p. 1
• The appropriate error-rate measure depends on the application: pretrial risk assessment may equalize false positive rates, while loan approval may equalize false negative rates.False discovery and false omission rates may also be used depending on the scenario and misclassification costs (see Table 1).Source: §1 · pp. 1–2
• The paper develops disparate-mistreatment measures for decision-boundary classifiers and incorporates them as convex-concave constraints solvable with convex-concave programming [26].Its experiments on synthetic and real-world datasets show that the methodology can be used to avoid disparate mistreatment.Source: §1 · p. 2

BACKGROUND AND RELATED WORK

• Different group error rates constitute disparate mistreatment: C1 has male/female false-negative rates of 0.0 and 0.5, while C2 also has false-positive rates of 0.0 and 1.0.Source: §2 · p. 2
• Disparate treatment occurs when people with the same or similar non-sensitive features receive different outputs because their sensitive attributes differ.Source: §2 · p. 2
• Disparate impact concerns groups receiving beneficial or harmful outcomes at different rates; it can help when ground truth is unavailable but mislead when valid decisions are known.Because outcome proportionality can disregard justifiable differences such as candidate qualifications, disparate impact risks reverse discrimination; disparate mistreatment can instead assess error disparities when decision correctness is known.Source: §2 · pp. 2–3
• Prior studies proposed detecting and removing unfairness defined by disparate treatment or impact, while Goel et al. used ground truth to identify higher false-positive stop rates for Black people than White people.The findings support the need for decision systems without disparate mistreatment.Source: §2 · p. 3
• Hardt et al. [15] proposed post-processing classifier probabilities with group-specific thresholds to achieve equivalent fairness, but the method requires sensitive-attribute information at decision time.That requirement prevents use when such information is unavailable for privacy reasons or prohibited by disparate-treatment laws.Source: §2 · p. 3

• The setup learns a decision boundary to classify feature vectors, assuming a binary sensitive feature while allowing generalization to categorical or multiple sensitive features.Source: §3 · p. 3
• Disparate treatment is absent when a classifier’s output probabilities given a feature vector do not change after observing the sensitive feature.Source: §3 · p. 3
• Disparate impact is absent when the probability of a positive prediction is equal across the two sensitive-feature groups.Source: §3 · p. 3
• Disparate mistreatment requires equal group error rates, measured by overall misclassification, FPR, FNR, FOR, or FDR.FPR and FNR are measured over true-label classes, while FOR and FDR are measured over predicted-label classes.Source: §3 · p. 3
• The proposed method targets simultaneous disparate treatment and mistreatment measured by overall error, FPR, and FNR, but leaves FOR and FDR for future work.The paper cites computational complexity as the challenge for eliminating mistreatment defined by FOR and FDR.Source: §3 · p. 4
• When group positive-label prevalence differs, equal calibration and equal false-positive and false-negative rates cannot generally all hold, so the paper allows bounded rate differences.The passage describes an exception for a classifier assigning all examples to one class and introduces a threshold ϵ for differences in the rates targeted by its method.Source: §3 · p. 4

4. CLASSIFIERS WITHOUT DISPARATE MISTREATMENT

• The direct approach constrains group misclassification-rate differences within ±ϵ, but the resulting fairness conditions are generally non-convex.Smaller ϵ specifies a more demanding fairness constraint.Source: §4 · p. 4
• A covariance proxy measures mistreatment through the association between sensitive attributes and misclassified users’ signed distances to the decision boundary; near-zero covariance indicates approximate fairness.For linear classifiers, the signed distance term reduces to θ^T x.Source: §4 · p. 4

Solving the problem efficiently

• Rewriting the proxy constraints yields a DCCP for any convex loss, solvable efficiently with heuristics such as Shen et al. [26].Separate constraints can target equal false positive and equal false negative rates.Source: §4 · pp. 4–5

Logistic regression without disparate mistreatment

• The general formulation is specialized to logistic regression, whose fair classifier is trained by constrained maximum-likelihood optimization.The unconstrained training objective minimizes the negative log-likelihood.Source: §4 · p. 5

Simultaneously removing disparate treatment

• Keeping decision-time features x disjoint from sensitive attribute z allows the formulation to remove disparate mistreatment and disparate treatment simultaneously.Source: §4 · p. 5

5. EVALUATION

• Experiments use logistic regression, five random 50/50 train-test splits, and average accuracy and fairness statistics; disparities are group differences in false positive and false negative rates, with values nearer zero indicating less mistreatment.The evaluation describes the two measures as DF P R and DF N R.Source: §5 · p. 5

5.1 Experiments on synthetic data

• 0.85 accuracy with the unconstrained synthetic classifier co-occurred with DF P R = 0.19; as the covariance constraint approaches zero, group false positive rates converge while accuracy falls.DF N R remains close to zero in this data distribution, though the paper notes this may vary with the underlying distribution.Source: §5.1 · pp. 5–6, Figure 2 · p. 6
• When synthetic DF P R and DF N R have opposite signs, constraining either error rate also reduces disparate mistreatment on the other, owing to shifted group cluster centroids.The effect is illustrated for data where one group has a higher false positive rate but a lower false negative rate.Source: §5.1 · p. 6, Figure 3 · p. 7
• When both synthetic disparities have the same sign, constraining only one rate can worsen the other; constraining both brings DF P R and DF N R near zero but causes a large accuracy drop.A single-rate constraint causes only a minor accuracy drop in this scenario.Source: §5.1 · pp. 6–7, Figure 4 · p. 7

5.1.3 Performance Comparison

• Our method matches Hardt et al. when both use sensitive and non-sensitive features, while avoiding disparate treatment at only about 5% additional accuracy cost; the baseline sometimes fails to achieve fairness.The comparison also reports that when the baseline achieves fairness, it can incur a much greater accuracy cost than competing methods.Source: §5.1.3 · pp. 7–8, Figure 5 · p. 8, Table 2 · p. 9

5.2 Real world dataset: ProPublica COMPAS

• 0.668 accuracy on COMPAS accompanied false positive rates of 0.35 for blacks and 0.17 for whites (DF P R = 0.18), and false negative rates of 0.31 and 0.61 (DF NR = −0.30).All three methods achieve similar accuracy at a given fairness level, and constraining either error rate also helps reduce disparate mistreatment on the other rate.Source: §5.2 · p. 8, Table 2 · p. 9
• On COMPAS, our method and the baseline do not reach zero DF P R or DF N R, likely because the small dataset weakens covariance estimates; Hardt et al. reaches both zero under joint constraints but at considerable accuracy cost.The training set contains 2,639 examples; the paper expects more reliable covariance estimates with sufficiently large training data.Source: §5.2 · pp. 8–9, Table 2 · p. 9

6. DISCUSSION AND FUTURE WORK

• The method trades off disparate-mistreatment fairness and accuracy while also allowing disparate treatment to be avoided, useful when sensitive attributes are unavailable or legally prohibited.The paper notes privacy as one reason sensitive-attribute information may be unavailable.Source: §6 · p. 9
• Extending the formulation beyond false-positive and false-negative rates to include false-discovery and false-omission rates is a natural but computationally non-trivial next step.The current formulations address disparate mistreatment only through false-positive and false-negative rates.Source: §6 · p. 9
• The fairness-constrained training formulation uses heuristic-solvable DCCP rather than convex optimization, so it lacks global-optimality guarantees [26].It also estimates analytical covariance with Monte Carlo covariance on the training set, which may be inaccurate when datasets are small.Source: §6 · p. 9