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# Metric-Fair Classifier Derandomization

*Proceedings of the 39th International Conference on Machine Learning*, PMLR 162:23999-24016, 2022.

#### Abstract

We study the problem of

*classifier derandomization*in machine learning: given a stochastic binary classifier $f: X \to [0,1]$, sample a deterministic classifier $\hat{f}: X \to \{0,1\}$ that approximates the output of $f$ in aggregate over any data distribution. Recent work revealed how to efficiently derandomize a stochastic classifier with strong output approximation guarantees, but at the cost of individual fairness — that is, if $f$ treated similar inputs similarly, $\hat{f}$ did not. In this paper, we initiate a systematic study of classifier derandomization with metric fairness guarantees. We show that the prior derandomization approach is almost maximally metric-unfair, and that a simple “random threshold” derandomization achieves optimal fairness preservation but with weaker output approximation. We then devise a derandomization procedure that provides an appealing tradeoff between these two: if $f$ is $\alpha$-metric fair according to a metric $d$ with a locality-sensitive hash (LSH) family, then our derandomized $\hat{f}$ is, with high probability, $O(\alpha)$-metric fair and a close approximation of $f$. We also prove generic results applicable to all (fair and unfair) classifier derandomization procedures, including a bias-variance decomposition and reductions between various notions of metric fairness.