  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.
