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Poster
in
Workshop: Algorithmic Fairness through the Lens of Causality and Privacy

Minimax Optimal Fair Regression under Linear Model

Kazuto Fukuchi · Jun Sakuma


Abstract: We investigate the minimax optimal error of a fair regression problem under a linear model employing demographic parity as a fairness constraint. As a tractable demographic parity constraint, we introduce (α,δ)-fairness consistency, meaning that the quantified unfairness is decreased at most nα rate with at least probability 1δ, where n is the sample size. In other words, the consistently fair algorithm eventually outputs a regressor satisfying the demographic parity constraint with high probability as n tends to infinity. As a result of our analyses, we found that the minimax optimal error under the (α,δ)-fairness consistency constraint is Θ(dMn) provided that α12, where d is the dimensionality, and M is the number of groups induced from the sensitive attributes.

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