We study the problem of fair binary classification using the notion of Equal Opportunity. It requires the true positive rate to distribute equally across the sensitive groups. Within this setting we show that the fair optimal classifier is obtained by recalibrating the Bayes classifier by a group-dependent threshold. We provide a constructive expression for the threshold. This result motivates us to devise a plug-in classification procedure based on both unlabeled and labeled datasets. While the latter is used to learn the output conditional probability, the former is used for calibration. The overall procedure can be computed in polynomial time and it is shown to be statistically consistent both in terms of classification error and fairness measure. Finally, we present numerical experiments which indicate that our method is often superior or competitive with the state-of-the-art methods on benchmark datasets.
To the best of our knowledge the formula for the optimal fair classifier presented here is novel. In the authors note that the optimal equalized odds or equal opportunity classifier can be derived from the Bayes optimal regressor, however, no explicit expression for this threshold is provided. The idea of recalibrating the Bayes classifier is also discussed in a number of papers, see for example @cite_45 @cite_35 and references therein. More importantly, the problem of deriving and estimators under fairness constraints has received limited attention in the literature. In @cite_15 , the authors present consistency results under restrictive assumptions on the model class. Furthermore, they only consider convex approximations of the risk and fairness constraint and it is not clear how to relate their results to the original problem with the miss-classification risk. @cite_31 , the authors reduce the problem of fair classification to a sequence of cost-sensitive problems by leveraging the saddle point formulation. They show that their algorithm is consistent in both risk and fairness constraints. However, similarly to @cite_15 , the authors of @cite_31 assume that the family of possible classifiers admits a bounded Rademacher complexity.
@cite_35 @cite_15 @cite_45 @cite_31
2790025105 2963803533 2963178340 2790744245
We address the problem of algorithmic fairness: ensuring that sensitive variables do not unfairly influence the outcome of a classifier. We present an approach based on empirical risk minimization, which incorporates a fairness constraint into the learning problem. It encourages the conditional risk of the learned classifier to be approximately constant with respect to the sensitive variable. We derive both risk and fairness bounds that support the statistical consistency of our approach. We specify our approach to kernel methods and observe that the fairness requirement implies an orthogonality constraint which can be easily added to these methods. We further observe that for linear models the constraint translates into a simple data preprocessing step. Experiments indicate that the method is empirically effective and performs favorably against state-of-the-art approaches. The machine learning community has become increasingly concerned with the potential for bias and discrimination in predictive models. This has motivated a growing line of work on what it means for a classification procedure to be "fair." In this paper, we investigate the tension between minimizing error disparity across different population groups while maintaining calibrated probability estimates. We show that calibration is compatible only with a single error constraint (i.e. equal false-negatives rates across groups), and show that any algorithm that satisfies this relaxation is no better than randomizing a percentage of predictions for an existing classifier. These unsettling findings, which extend and generalize existing results, are empirically confirmed on several datasets. We present a systematic approach for achieving fairness in a binary classification setting. While we focus on two well-known quantitative definitions of fairness, our approach encompasses many other previously studied definitions as special cases. The key idea is to reduce fair classification to a sequence of cost-sensitive classification problems, whose solutions yield a randomized classifier with the lowest (empirical) error subject to the desired constraints. We introduce two reductions that work for any representation of the cost-sensitive classifier and compare favorably to prior baselines on a variety of data sets, while overcoming several of their disadvantages.