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How Far Can Fairness Constraints Help Recover From Biased Data?
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Generalizes Blum & Stangl's result that equal-opportunity-constrained classifiers on extremely biased data recover the optimal fair classifier, via linear fractional transformations of the regression function, extending to Massart noise, reject-option classifiers, arbitrary distributions/hypothesis classes (robust hypotheses), and time-varying bias.
Problem
Whether fair classification with equal opportunity constraints on biased training data (under-representation and label bias) can recover the optimal accurate and fair classifier on the original distribution, and under what conditions, beyond the stylized i.i.d. noise setting of Blum & Stangl.
Approach
Observes that common data bias models transform the regression function by a linear fractional transformation that is order-preserving, so group-dependent thresholds on the original regression function characterize the optimal fair classifier on biased data; this yields necessary-and-sufficient recovery conditions and extensions to Massart noise, reject-option classifiers, arbitrary hypothesis cla
Key results
- Derives necessary and sufficient conditions (Theorem on i.i.d. noise) under which the optimal equal opportunity classifier on the biased distribution equals the Bayes optimal classifier, strengthening Blum & Stangl's Theorem 4.1.
- Extends recovery to Massart label noise and to optimal reject option classifiers on arbitrary distributions.
- For arbitrary distributions and hypothesis classes, shows recovery of epsilon-robust optimal classifiers under simple bias conditions, e.g., r=0.2, nu=0.1, epsilon=0.05 illustrated in a recovery region.
Surprising findings
- Under repeated application of the bias model with beta_n < 1, the underprivileged regression function goes to 0 as steps grow, so recovery fails in the infinite horizon.
- Demographic parity cannot recover the optimal classifier in a specific example where equal opportunity can.
Limitations
- Assumes discrete feature space and specific data bias models (under-representation and label bias).
- For arbitrary hypothesis classes, requires the optimal classifier to be epsilon-robust and fair.
- Time-varying results show recovery only holds for a bounded number of bias steps.
Experimental setup
Metrics: accuracy equal opportunity
Baselines: Blum & Stangl (2019)
Builds on: Blum & Stangl (2019) recovery result equal opportunity (Hardt et al.) Massart noise model
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