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From Parity to Preference-based Notions of Fairness in Classification

Muhammad Bilal Zafar, Isabel Valera, Manuel Gomez Rodriguez, Krishna P. Gummadi, Adrian Weller

arXiv:1707.00010v2stat.MLcs.LG

TL;DR

Parity-based fairness notions can trade off prediction accuracy against equal treatment or outcomes across groups. This paper introduces preference-based fairness notions, tractable classifier proxies, and experiments showing that they often improve decision accuracy relative to parity-based fairness.

  • Problem

    Existing parity-based fairness mechanisms can impose accuracy costs, reflecting tradeoffs between prediction accuracy and parity in treatment or impact.

  • Method

    The paper introduces preferred treatment and preferred impact, inspired by fair division and envy-freeness, and develops tractable proxies for boundary-based classifiers.

  • Results

    Preference-based fairness often allows greater decision accuracy than existing parity-based fairness notions across synthetic and real-world datasets.

  • Takeaways & Limitations

    Preferred treatment relaxes treatment parity and permits group-conditional decision making when feature predictive power differs substantially across sensitive groups.

  • Takeaways & Limitations

    The paper focuses on group preferences and leaves individual preferences and their implications for the cost of achieving fairness for future work.

Abstract

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The adoption of automated, data-driven decision making in an ever expanding range of applications has raised concerns about its potential unfairness towards certain social groups. In this context, a number of recent studies have focused on defining, detecting, and removing unfairness from data-driven decision systems. However, the existing notions of fairness, based on parity (equality) in treatment or outcomes for different social groups, tend to be quite stringent, limiting the overall decision making accuracy. In this paper, we draw inspiration from the fair-division and envy-freeness literature in economics and game theory and propose preference-based notions of fairness -- given the choice between various sets of decision treatments or outcomes, any group of users would collectively prefer its treatment or outcomes, regardless of the (dis)parity as compared to the other groups. Then, we introduce tractable proxies to design margin-based classifiers that satisfy these preference-based notions of fairness. Finally, we experiment with a variety of synthetic and real-world datasets and show that preference-based fairness allows for greater decision accuracy than parity-based fairness.

1 Introduction

Parity-based fairness notions seek equality in treatment or impact but can constrain accuracy. The paper proposes preference-based alternatives that retain group-level fairness properties while permitting group-conditional decisions and potentially higher accuracy.

  • Motivation: Existing fairness notions require parity in treatment, impact, or both, often prohibiting group-conditional decision making.Treatment parity commonly requires systems to avoid using sensitive-attribute membership.
  • Motivation: Parity-based mechanisms can incur significant accuracy costs because high prediction accuracy and treatment or impact parity may trade off.The paper identifies both theoretical and empirical tradeoffs between accuracy and parity.
  • Preference-based fairness: Preference-based fairness asks each group to prefer its received decision outcomes over relevant alternative outcomes, drawing on fair division and envy-freeness.The proposed notions compare group benefits rather than requiring equal benefits across groups.
  • Preferred treatment: Preferred treatment relaxes treatment parity while allowing group-conditional decision making when feature predictive power differs substantially across groups.It retains group-level envy-freeness: no group would collectively benefit from switching its sensitive-group membership.
  • Preferred impact: Preferred impact relaxes impact parity, guaranteeing each group at least as many beneficial outcomes as under impact parity while allowing disparities in benefits.The paper links strict impact parity to reduced beneficial outcomes and lower overall decision accuracy in some scenarios.
  • Scope: Preference-based fairness is not suitable in every scenario, because parity fairness may remain the eventual or more desirable goal.The authors explicitly limit the universality of their preference-based notions.
  • Approach and evaluation: The paper formalizes these notions, develops tractable proxies for convex margin-based classifiers, and evaluates them on synthetic and real-world datasets.It reports significant gains in overall decision-making accuracy compared with parity-based fairness.

2 Defining preference-based fairness for classification

The paper defines utility and group benefit for binary classification, then replaces parity requirements with group-level preference conditions that permit disparities while preserving beneficial outcomes.

  • Quality metrics: Utility measures the decision maker’s overall profit, while group benefit measures the fraction of beneficial outcomes received by users sharing sensitive attribute value z.The paper uses overall accuracy as a simple utility example and allows group benefit to be conditioned on users’ true labels.
  • Parity-based fairness: Impact parity requires equal group benefits across all sensitive attribute values, and many related fairness terms instantiate this same equality requirement.Examples include disparate impact, indirect discrimination, redlining, statistical parity, disparate mistreatment, and equality of opportunity.
  • Fairness beyond parity: Preferred treatment requires each group to benefit at least as much from its own group-conditional classifier as from any other group’s classifier.A classifier without group-conditional decisions automatically satisfies preferred treatment; group-level envy-freeness motivates the criterion.
  • Fairness beyond parity: Preferred impact compares a classifier with an impact-parity classifier and requires higher group benefit for every sensitive-attribute group.The condition is inspired by bargaining over beneficial outcomes relative to a baseline allocation.
  • Scope: The paper studies group preferences: collectively preferred outcomes may disadvantage some individuals, while individual-preference extensions are left for future work.The proposed notions therefore do not require every individual within a group to prefer the group’s selected outcomes.

3 Training preferred classifiers

The training procedure maximizes empirical utility subject to preferred-impact or preferred-treatment constraints, using linear convex classifiers and tractable convex-concave approximations.

  • Optimization setup: The training problems learn group-conditional classifiers that maximize utility from a dataset, using empirical estimates of utility and group benefits.The preferred-impact constraints use precomputable benefits from an impact-parity classifier, whereas preferred-treatment constraints contain optimization variables on both sides.
  • Assumptions: The method assumes convex boundary-based classifiers, specializes exposition to linear classifiers, defines utility as overall accuracy, and defines group benefit through positive-class probabilities.The linearity assumption is relaxed for a non-linear SVM in Appendix A.
  • Limitations and future work: The paper assumes convex boundary-based classifiers and identifies extending the methodology to neural networks and decision trees as future work.It also identifies relaxing the stated assumptions as an open direction.
  • Tractable proxies: Because the original objectives and constraints are nonconvex, the method replaces them with a convex loss and ramp-based group-benefit approximations.The resulting formulations are disciplined convex-concave programs that can be efficiently solved with established heuristics.
  • Classifier implementations: The preferred-classifier constraints can be incorporated into convex boundary-based models including linear SVM, with non-linear SVM extensions described in Appendix A.The paper also gives a logistic-regression specialization using an L2-norm regularizer.

4 Evaluation

The evaluation compares unconstrained, parity-based, and preference-based classifiers on synthetic and real-world datasets. Preference-based criteria generally preserve more accuracy than parity, although enforcing both can reduce accuracy on some datasets.

  • The experiments compare unconstrained, parity, preferred-treatment, preferred-impact, and preferred-both classifiers using accuracy and group benefits.
  • Synthetic data: 0.87 versus 0.57: the synthetic-data accuracy falls sharply from Uncons to Parity.The Uncons benefits are 0.16 and 0.85 for the two groups, while Parity satisfies both parity criteria.
  • Synthetic data: 0.76 versus 0.57: Preferred impact achieves higher synthetic-data accuracy than Parity and provides higher benefits for both groups.Preferred impact does not satisfy preferred treatment because group-1 would benefit more from group-0’s classifier, 0.96 versus 0.86.
  • Real-world datasets: On real datasets, Preferred treatment matches Uncons accuracy and exceeds Parity, while Preferred impact also exceeds Parity, especially on SQF.Preferred treatment does not meet preferred impact, and Preferred impact does not always satisfy preferred treatment.
  • Real-world datasets: Preferred both outperforms Parity on COMPAS and SQF but is slightly worse on Adult; enforcing both criteria can therefore impose larger dataset-dependent accuracy losses.The authors hypothesize that splitting samples among group-conditional classifiers may partly explain the loss.

5 Conclusion

The paper introduces preference-based fairness notions connected to envy-freeness and evaluates tractable classifier proxies. It concludes that preference-based fairness often improves accuracy over parity, while noting important scope and appropriateness boundaries.

  • The paper introduces preferred treatment and preferred impact, connecting fairness-aware machine learning with envy-freeness and bargaining.
  • Tractable proxies enable boundary-based classifiers satisfying the proposed fairness notions, which are evaluated on synthetic and real-world datasets.
  • Preference-based fairness often allows greater decision accuracy than existing parity-based fairness notions.
  • The methodology is limited to convex boundary-based classifiers, leaving neural networks and decision trees for future extension.
  • Parity-based fairness may remain preferable in scenarios where parity is the eventual goal.

A Particularizing fairness constraints for non-linear SVM

The appendix specializes the nonlinear SVM formulation for preferred-impact and preferred-treatment classifiers. It uses the standard dual optimization variables and group-specific Gram matrices and label vectors.

  • The nonlinear SVM dual solves for α under box and equality constraints to specify the decision boundary.
  • The classifier uses G as an N × N Gram matrix with Gi,j = yiyjk(xi, xj), where the kernel is an inner product of transformed features.
  • For an unknown x, prediction is sign(α(x)), with α(x) interpreted as signed distance from the decision boundary.
  • Preferred-impact classifiers: Preferred-impact nonlinear SVMs particularize the standard formulation using parity-impact classifiers and group-specific Gram matrices and label vectors.
  • Preferred-treatment classifiers: The same specialization is applied to train group-conditional preferred-treatment nonlinear SVMs, and the constraints can also be added in primal form.

B Experimental details

Regularization is selected using train-validation splits, with separate procedures for unconstrained, parity, and preferentially fair classifiers. Hard zero-tolerance constraints can produce divergent group benefits on real data.

  • Training data are split into 70% Dtr and 30% Dval to select optimal L2 regularization parameters from candidate values.
  • Classifier training: Unconstrained classifiers train separately for each sensitive group, whereas parity classifiers train one classifier across all groups.
  • Classifier training: The selected λopt maximizes validation accuracy, after which the classifier is retrained on the full training dataset.
  • Classifier training: Preferentially fair classifiers jointly minimize both groups’ objective functions while satisfying fairness constraints, selecting λ0 and λ1 combinations by validation accuracy.
  • Constraint tolerance: Hard thresholds without tolerance can yield divergent group benefits on real-world datasets, possibly because Dtr and Dval vary.

C Experiments with non-linear SVM

The nonlinear SVM experiment compares unconstrained, parity-based, and preference-based classifiers on a synthetic non-linearly separable dataset. Preference-based constraints reduce unfairness with smaller accuracy costs than parity constraints.

  • Setup: The experiment uses an RBF-kernel SVM on a non-linearly separable synthetic dataset.The dataset contains 4,000 binary class labels and two-dimensional feature vectors generated from class-conditional Gaussian mixtures.
  • Results: The parity classifier satisfies treatment and impact parity, but accuracy drops from 0.96 for Uncons to 0.61 for Parity.Both groups use the same classifier under the treatment-parity condition.
  • Results: The unconstrained classifier achieves 0.96 accuracy but produces group benefits of 0.07 versus 0.87 and violates preferred treatment.Group-0 benefits would rise from 0.07 to 0.17 under group-1’s classifier.
  • Results: The preferred treatment classifier removes group-0 envy while reducing accuracy only from 0.96 to 0.93.It adjusts the decision boundary for group-0 to eliminate the preference violation.
  • Results: The preferred impact classifier gives both groups higher or equal benefits than the parity classifier at an accuracy of 0.84 versus 0.61.In this experiment, it also satisfies the preferred treatment criterion.

D Dataset statistics

This section describes real-world fairness datasets and identifies the statistics summarized in the COMPAS, Adult, and NYPD SQF tables.

  • COMPAS: The COMPAS table reports recidivism rates for both races in the ProPublica COMPAS data.The COMPAS classification task concerns recidivism within two years.
  • NYPD SQF: The original NYPD SQF table reports people found possessing a weapon in the 2012 dataset.The SQF task predicts whether a stopped pedestrian suspected of carrying a weapon actually possesses one.
  • NYPD SQF: The class-balanced NYPD SQF table reports weapon-possession outcomes after balancing the class distribution.The majority positive class was subsampled to match the minority negative class.
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