A Unified Post-Processing Framework for Group Fairness in Classification

TL;DR

This work presents LinearPost, a unified post-processing framework that achieves group fairness across statistical parity, equal opportunity, and equalized odds in multiclass and both attribute-aware and attribute-blind settings. The key idea is to express the Bayes-optimal fair classifier as a linear post-processing of the Bayes-optimal score, with a fairness risk term built from a Bayes-optimal group predictor and weights derived from the dual of an empirical linear program. The authors establish conditions (notably a random perturbation to ensure uniqueness and multicalibration of the group predictor) under which this representation holds, and provide a practical algorithm that estimates the risk and group predictor, calibrates when needed, and solves an empirical LP to obtain post-processing weights. Empirical results demonstrate that LinearPost yields favorable accuracy-fairness tradeoffs, especially in high fairness regimes and multiclass tasks, often outperforming existing post-processing and in-processing methods while highlighting the importance of calibration and attribute-awareness for achieving stronger fairness guarantees.

Abstract

We present a post-processing algorithm for fair classification that covers group fairness criteria including statistical parity, equal opportunity, and equalized odds under a single framework, and is applicable to multiclass problems in both attribute-aware and attribute-blind settings. Our algorithm, called "LinearPost", achieves fairness post-hoc by linearly transforming the predictions of the (unfair) base predictor with a "fairness risk" according to a weighted combination of the (predicted) group memberships. It yields the Bayes optimal fair classifier if the base predictors being post-processed are Bayes optimal, otherwise, the resulting classifier may not be optimal, but fairness is guaranteed as long as the group membership predictor is multicalibrated. The parameters of the post-processing can be efficiently computed and estimated from solving an empirical linear program. Empirical evaluations demonstrate the advantage of our algorithm in the high fairness regime compared to existing post-processing and in-processing fair classification algorithms.

Figures (12)

• Figure 1: Tradeoffs between accuracy and fairness on Adult subject to SP, TPR (binary class equal opportunity), or EO, respectively. Fairness violation is computed uniformly (see definitions in \ref{['tab:equivalence']}). Average of five random seeds.
• Figure 2: Tradeoffs between accuracy and fairness on COMPAS. TPR is binary class equal opportunity.
• Figure 3: Tradeoffs between accuracy and fairness on ACSIncome2. TPR is binary class equal opportunity.
• Figure 4: Tradeoffs between accuracy and fairness on ACSIncome5. MC EOpp is multiclass equal opportunity.
• Figure 5: Tradeoffs between accuracy and fairness on BiasBios. MC EOpp is multiclass equal opportunity. Due to the large number of classes, to highlight incremental improvements, fairness violation is computed by taking the root mean square of the disparities (across $y\in\mathcal{Y}$ for SP and EOpp, and $y,y'\in\mathcal{Y}$ for EO). The RMS violation of MC EOpp is the same as the $\mathit{GAP}^{\textrm{TPR},\textrm{RMS}}$ metric in ravfogel2020NullItOut.

Theorems & Definitions (32)

• definition 1: Group Fairness
• remark 1
• theorem 1: Representation
• proof : Proof of \ref{['thm:opt.fair']}
• proposition 1
• remark 2: Scenarios Where \ref{['ass:uniqueness']} Fails
• remark 3: Impact of Randomization on Individual Fairness
• theorem 2: Sensitivity
• corollary 1: Multicalibration
• theorem 3: Sample Complexity