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Algorithmic fairness, and in particular the fairness of scoring and classification algorithms, has become a topic of increasing social concern and has recently witnessed an explosion of research in theoretical computer science, machine learning, statistics, the social sciences, and law. Much of the literature considers the case of a single classifier (or scoring function) used once, in isolation. In this work, we initiate the study of the fairness properties of systems composed of algorithms that are fair in isolation; that is, we study fairness under composition. We identify pitfalls of naive composition and give general constructions for fair composition, demonstrating both that classifiers that are fair in isolation do not necessarily compose into fair systems and also that seemingly unfair components may be carefully combined to construct fair systems. We focus primarily on the individual fairness setting proposed in [Dwork, Hardt, Pitassi, Reingold, Zemel, 2011], but also extend our results to a large class of group fairness definitions popular in the recent literature, exhibiting several cases in which group fairness definitions give misleading signals under composition.
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In this work we study the problem of measuring the fairness of a machine learning model under noisy information. Focusing on group fairness metrics, we investigate the particular but common situation when the evaluation requires controlling for the confounding effect of covariate variables. In a practical setting, we might not be able to jointly observe the covariate and group information, and a standard workaround is to then use proxies for one or more of these variables. Prior works have demonstrated the challenges with using a proxy for sensitive attributes, and strong independence assumptions are needed to provide guarantees on the accuracy of the noisy estimates. In contrast, in this work we study using a proxy for the covariate variable and present a theoretical analysis that aims to characterize weaker conditions under which accurate fairness evaluation is possible. Furthermore, our theory identifies potential sources of errors and decouples them into two interpretable parts $gamma$ and $epsilon$. The first part $gamma$ depends solely on the performance of the proxy such as precision and recall, whereas the second part $epsilon$ captures correlations between all the variables of interest. We show that in many scenarios the error in the estimates is dominated by $gamma$ via a linear dependence, whereas the dependence on the correlations $epsilon$ only constitutes a lower order term. As a result we expand the understanding of scenarios where measuring model fairness via proxies can be an effective approach. Finally, we compare, via simulations, the theoretical upper-bounds to the distribution of simulated estimation errors and show that assuming some structure on the data, even weak, is key to significantly improve both theoretical guarantees and empirical results.
Algorithmic risk assessments are used to inform decisions in a wide variety of high-stakes settings. Often multiple predictive models deliver similar overall performance but differ markedly in their predictions for individual cases, an empirical phenomenon known as the Rashomon Effect. These models may have different properties over various groups, and therefore have different predictive fairness properties. We develop a framework for characterizing predictive fairness properties over the set of models that deliver similar overall performance, or the set of good models. Our framework addresses the empirically relevant challenge of selectively labelled data in the setting where the selection decision and outcome are unconfounded given the observed data features. Our framework can be used to 1) replace an existing model with one that has better fairness properties; or 2) audit for predictive bias. We illustrate these uses cases on a real-world credit-scoring task and a recidivism prediction task.
Training and evaluation of fair classifiers is a challenging problem. This is partly due to the fact that most fairness metrics of interest depend on both the sensitive attribute information and label information of the data points. In many scenarios it is not possible to collect large datasets with such information. An alternate approach that is commonly used is to separately train an attribute classifier on data with sensitive attribute information, and then use it later in the ML pipeline to evaluate the bias of a given classifier. While such decoupling helps alleviate the problem of demographic scarcity, it raises several natural questions such as: how should the attribute classifier be trained?, and how should one use a given attribute classifier for accurate bias estimation? In this work we study this question from both theoretical and empirical perspectives. We first experimentally demonstrate that the test accuracy of the attribute classifier is not always correlated with its effectiveness in bias estimation for a downstream model. In order to further investigate this phenomenon, we analyze an idealized theoretical model and characterize the structure of the optimal classifier. Our analysis has surprising and counter-intuitive implications where in certain regimes one might want to distribute the error of the attribute classifier as unevenly as possible among the different subgroups. Based on our analysis we develop heuristics for both training and using attribute classifiers for bias estimation in the data scarce regime. We empirically demonstrate the effectiveness of our approach on real and simulated data.
In this paper, we study the problem of fair classification in the presence of prior probability shifts, where the training set distribution differs from the test set. This phenomenon can be observed in the yearly records of several real-world datasets, such as recidivism records and medical expenditure surveys. If unaccounted for, such shifts can cause the predictions of a classifier to become unfair towards specific population subgroups. While the fairness notion called Proportional Equality (PE) accounts for such shifts, a procedure to ensure PE-fairness was unknown. In this work, we propose a method, called CAPE, which provides a comprehensive solution to the aforementioned problem. CAPE makes novel use of prevalence estimation techniques, sampling and an ensemble of classifiers to ensure fair predictions under prior probability shifts. We introduce a metric, called prevalence difference (PD), which CAPE attempts to minimize in order to ensure PE-fairness. We theoretically establish that this metric exhibits several desirable properties. We evaluate the efficacy of CAPE via a thorough empirical evaluation on synthetic datasets. We also compare the performance of CAPE with several popular fair classifiers on real-world datasets like COMPAS (criminal risk assessment) and MEPS (medical expenditure panel survey). The results indicate that CAPE ensures PE-fair predictions, while performing well on other performance metrics.
We study the problem of learning fair prediction models for unseen test sets distributed differently from the train set. Stability against changes in data distribution is an important mandate for responsible deployment of models. The domain adaptation literature addresses this concern, albeit with the notion of stability limited to that of prediction accuracy. We identify sufficient conditions under which stable models, both in terms of prediction accuracy and fairness, can be learned. Using the causal graph describing the data and the anticipated shifts, we specify an approach based on feature selection that exploits conditional independencies in the data to estimate accuracy and fairness metrics for the test set. We show that for specific fairness definitions, the resulting model satisfies a form of worst-case optimality. In context of a healthcare task, we illustrate the advantages of the approach in making more equitable decisions.
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