Inherent Tradeoffs in Learning Fair Representations (1906.08386v6)

Published 19 Jun 2019 in cs.LG, cs.AI, and stat.ML

Abstract: Real-world applications of machine learning tools in high-stakes domains are often regulated to be fair, in the sense that the predicted target should satisfy some quantitative notion of parity with respect to a protected attribute. However, the exact tradeoff between fairness and accuracy is not entirely clear, even for the basic paradigm of classification problems. In this paper, we characterize an inherent tradeoff between statistical parity and accuracy in the classification setting by providing a lower bound on the sum of group-wise errors of any fair classifiers. Our impossibility theorem could be interpreted as a certain uncertainty principle in fairness: if the base rates differ among groups, then any fair classifier satisfying statistical parity has to incur a large error on at least one of the groups. We further extend this result to give a lower bound on the joint error of any (approximately) fair classifiers, from the perspective of learning fair representations. To show that our lower bound is tight, assuming oracle access to Bayes (potentially unfair) classifiers, we also construct an algorithm that returns a randomized classifier that is both optimal (in terms of accuracy) and fair. Interestingly, when the protected attribute can take more than two values, an extension of this lower bound does not admit an analytic solution. Nevertheless, in this case, we show that the lower bound can be efficiently computed by solving a linear program, which we term as the TV-Barycenter problem, a barycenter problem under the TV-distance. On the upside, we prove that if the group-wise Bayes optimal classifiers are close, then learning fair representations leads to an alternative notion of fairness, known as the accuracy parity, which states that the error rates are close between groups. Finally, we also conduct experiments on real-world datasets to confirm our theoretical findings.

Authors (2)

Han Zhao (159 papers)
Geoffrey J. Gordon (30 papers)

Citations (200)

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Summary

Essay on "Inherent Tradeoffs in Learning Fair Representations"

The paper "Inherent Tradeoffs in Learning Fair Representations" by Han Zhao and Geoffrey J. Gordon presents a theoretical exploration into the intrinsic tensions between fairness and accuracy in machine learning models, specifically within the context of classification tasks. The authors focus on the popular fairness criterion known as statistical parity and investigate the consequences of imposing this constraint on classification accuracy.

Key Contributions

The principal contribution of this work is the formal characterization of a tradeoff between statistical parity and accuracy. The authors derive an information-theoretic lower bound on the sum of group-wise errors that any fair classifier must incur. This lower bound highlights an essential tension akin to an uncertainty principle in fairness; it indicates that if the base rates differ among groups, any classifier that satisfies statistical parity will necessarily have a large error on at least one of those groups.

The authors further extend their analysis to a more complex situation where the protected attribute can take more than two values. In this multi-class setting, an analytic solution for the lower bound is not feasible. However, they show that this bound can be efficiently computed through a linear programming problem termed the TV-Barycenter problem.

Additionally, assuming oracle access to Bayes (perhaps biased) classifiers for each group, the authors propose an algorithm that constructs a randomized fair classifier, which is both optimal (in terms of accuracy) and satisfies statistical parity. This construction reaffirms the tightness of their proposed lower bounds.

Theoretical Implications

From a theoretical standpoint, the results serve as a guide to understanding the inherent limitations of enforcing fairness through statistical parity in machine learning models. The concept that a perfect tradeoff-free model does not exist (when groups have different base rates) challenges a significant portion of the existing work on fair machine learning, which often assumes that fairness constraints can always be implemented without significant repercussions on model performance.

The extension to a multi-class protected attribute demonstrates the complexity and computational demands of fairness constraints in real-world settings, where the classes are often multidimensional rather than binary.

Empirical Validation and Future Directions

To empirically validate their theoretical findings, Zhao and Gordon conduct experiments on a real-world dataset using adversarial debiasing methods to learn fair representations. Their experiments corroborate the theoretical tradeoff established and highlight the difficulty of simultaneously achieving low joint error rates and perfect statistical parity.

This research opens multiple avenues for future exploration in AI fairness. Notably, there is potential to investigate alternative fairness definitions that might offer more balanced tradeoffs or contexts where such tradeoffs could be mitigated through domain-specific techniques or data augmentation.

Conclusion

In conclusion, Zhao and Gordon’s paper provides a rigorous foundation for understanding and quantifying the costs of fairness in machine learning, particularly when using statistical parity. Their work enriches the conversation around fairness in AI by providing concrete bounds and prompting further inquiry into machine learning models that account for fairness without disproportionate accuracy loss. Future research should continue to explore diversified fairness metrics that may present more favorable tradeoffs or develop algorithms that mitigate these tradeoffs under various conditions.

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