FAIREE: FAIR CLASSIFICATION WITH FINITE-SAMPLE AND DISTRIBUTION-FREE GUARANTEE

Abstract

Algorithmic fairness plays an increasingly critical role in machine learning research. Several group fairness notions and algorithms have been proposed. However, the fairness guarantee of existing fair classification methods mainly depends on specific data distributional assumptions, often requiring large sample sizes, and fairness could be violated when there is a modest number of samples, which is often the case in practice. In this paper, we propose FaiREE, a fair classification algorithm that can satisfy group fairness constraints with finite-sample and distribution-free theoretical guarantees. FaiREE can be adapted to satisfy various group fairness notions (e.g., Equality of Opportunity, Equalized Odds, Demographic Parity, etc.) and achieve the optimal accuracy. These theoretical guarantees are further supported by experiments on both synthetic and real data. FaiREE is shown to have favorable performance over state-of-the-art algorithms.



Among these fairness algorithms, postprocessing is a popular type of algorithm which modifies the output of the model to satisfy fairness constraints. However, recent post-processing algorithms are found to lack the ability to realize accuracy-fairness trade-off and perform poorly when the sample size is limited (Hardt et al., 2016; Pleiss et al., 2017) . In addition, since most fairness constraints are non-convex, some papers propose convex relaxation-based methods Zafar et al. (2017b); Krishnaswamy et al. (2021) . This type of algorithms generally do not have the theoretical guarantee of how the output satisfies the exact original fairness constraint. Another



algorithms have been increasingly used in consequential domains such as college admission Chouldechova & Roth (2018), loan application Ma et al. (2018), and disease diagnosis Fatima et al. (2017), there are emerging concerns about the algorithmic fairness in recent years. When standard machine learning algorithms are directly applied to the biased data provided by humans, the outputs are sometimes found to be biased towards certain sensitive attribute that we want to protect (race, gender, etc). To quantify the fairness in machine learning algorithms, many fairness notions have been proposed, including the individual fairness notion Biega et al. (2018), group fairness notions such as Demographic Parity, Equality of Opportunity, Predictive Parity, and Equalized Odds (Dieterich et al., 2016; Hardt et al., 2016; Gajane & Pechenizkiy, 2017; Verma & Rubin, 2018), and multi-group fairness notions including multi-calibration Hébert-Johnson et al. (2018) and multi-accuracy Kim et al. (2019). Based on these fairness notions or constraints, corresponding algorithms were designed to help satisfy the fairness constraints(Hardt et al., 2016; Pleiss et al., 2017; Zafar et al., 2017b; Krishnaswamy  et al., 2021; Valera et al., 2018; Chzhen et al., 2019; Zeng et al., 2022; Thomas et al., 2019).

Figure 1: Comparison of FairBayes and FaiREE on the synthetic data with sample size = 1000. See Table 2 for detailed numerical results. Left: DEOO v.s. α, Right: DEOO v.s. Test accuracy. Here, DEOO is the degree of violation to fairness constraint Equality of Opportunity and α is the prespecified desired level to upper bound DEOO for both methods. See Eq. (1) in Section 2 for a more detailed definition.

