Developing classification algorithms that are fair with respect to sensitive attributes of the data is an important problem due to the increased deployment of classification algorithms in societ al contexts. Several recent works have focused on studying classification with respect to specific fairness metrics, modeled the corresponding fair classification problem as constrained optimization problems, and developed tailored algorithms to solve them. Despite this, there still remain important metrics for which there are no fair classifiers with theoretical guarantees; primarily because the resulting optimization problem is non-convex. The main contribution of this paper is a meta-algorithm for classification that can take as input a general class of fairness constraints with respect to multiple non-disjoint and multi-valued sensitive attributes, and which comes with provable guarantees. In particular, our algorithm can handle non-convex "linear fractional" constraints (which includes fairness constraints such as predictive parity) for which no prior algorithm was known. Key to our results is an algorithm for a family of classification problems with convex constraints along with a reduction from classification problems with linear fractional constraints to this family. Empirically, we observe that our algorithm is fast, can achieve near-perfect fairness with respect to various fairness metrics, and the loss in accuracy due to the imposed fairness constraints is often small.
Beyond group fairness, recent works also proposed other fairness definitions concerned in classification. @cite_2 and @cite_40 discussed a notion of that similar individuals should be treated similarly. @cite_5 defined based on the concepts of fair division and envy-freeness in economics. Moreover, Grgi 'c -Hla c @cite_23 @cite_26 discussed that investigates which input features are fair to use in the decision process and how including or excluding the features would affect outcomes. Finally, Chouldechova @cite_12 and @cite_20 investigated the inherent tradeoff between equalized odds and predictive parity (called well-calibrated in their papers).
@cite_26 @cite_40 @cite_23 @cite_2 @cite_5 @cite_20 @cite_12
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The most prevalent notions of fairness in machine learning are statistical definitions: they fix a small collection of pre-defined groups, and then ask for parity of some statistic of the classifier across these groups. Constraints of this form are susceptible to intentional or inadvertent "fairness gerrymandering", in which a classifier appears to be fair on each individual group, but badly violates the fairness constraint on one or more structured subgroups defined over the protected attributes. We propose instead to demand statistical notions of fairness across exponentially (or infinitely) many subgroups, defined by a structured class of functions over the protected attributes. This interpolates between statistical definitions of fairness and recently proposed individual notions of fairness, but raises several computational challenges. It is no longer clear how to audit a fixed classifier to see if it satisfies such a strong definition of fairness. We prove that the computational problem of auditing subgroup fairness for both equality of false positive rates and statistical parity is equivalent to the problem of weak agnostic learning, which means it is computationally hard in the worst case, even for simple structured subclasses. We then derive two algorithms that provably converge to the best fair classifier, given access to oracles which can solve the agnostic learning problem. The algorithms are based on a formulation of subgroup fairness as a two-player zero-sum game between a Learner and an Auditor. Our first algorithm provably converges in a polynomial number of steps. Our second algorithm enjoys only provably asymptotic convergence, but has the merit of simplicity and faster per-step computation. We implement the simpler algorithm using linear regression as a heuristic oracle, and show that we can effectively both audit and learn fair classifiers on real datasets. 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. Discrimination via algorithmic decision making has received considerable attention. Prior work largely focuses on defining conditions for fairness, but does not define satisfactory measures of algorithmic unfairness. In this paper, we focus on the following question: Given two unfair algorithms, how should we determine which of the two is more unfair? Our core idea is to use existing inequality indices from economics to measure how unequally the outcomes of an algorithm benefit different individuals or groups in a population. Our work offers a justified and general framework to compare and contrast the (un)fairness of algorithmic predictors. This unifying approach enables us to quantify unfairness both at the individual and the group level. Further, our work reveals overlooked tradeoffs between different fairness notions: using our proposed measures, the overall individual-level unfairness of an algorithm can be decomposed into a between-group and a within-group component. Earlier methods are typically designed to tackle only between-group un- fairness, which may be justified for legal or other reasons. However, we demonstrate that minimizing exclusively the between-group component may, in fact, increase the within-group, and hence the overall unfairness. We characterize and illustrate the tradeoffs between our measures of (un)fairness and the prediction accuracy. Two food banks catering to populations of different sizes with different needs must divide among themselves a donation of food items. What constitutes a "fair" allocation of the items among them? Competitive equilibrium from equal incomes (CEEI) is a classic solution to the problem of fair and efficient allocation of goods among equally entitled agents [Foley 1967, Varian 1974]. Every agent (foodbank) receives an equal endowment of artificial currency with which to "purchase" bundles of goods (food items). Prices for the goods are set high enough such that the agents can simultaneously get their favorite within-budget bundle, and low enough such that all goods are allocated (no waste). A CEEI satisfies mathematical notions of fairness like fair-share, and also has built-in transparency -- prices can be published so the agents can verify they're being treated equally. However, a CEEI is not guaranteed to exist when the items are indivisible. We study competitive equilibrium from generic incomes (CEGI), which is based on the idea of slightly perturbed endowments, and enjoys similar fairness, efficiency and transparency properties as CEEI. We show that when the two agents have almost equal endowments and additive preferences for the items, a CEGI always exists. We then consider agents who are a priori non-equal (like different-sized foodbanks); we formulate a new notion of fair allocation among non-equals satisfied by CEGI, and show existence in cases of interest (like when the agents have identical preferences). Experiments on simulated and Spliddit data (a popular fair division website) indicate more general existence. Our results open opportunities for future research on fairness through generic endowments, and on fair treatment of non-equals.