  Recent works have investigated the sample complexity necessary for fair
machine learning. The most advanced of such sample complexity bounds are
developed by analyzing multicalibration uniform convergence for a given
predictor class. We present a framework which yields multicalibration error
uniform convergence bounds by reparametrizing sample complexities for Empirical
Risk Minimization (ERM) learning. From this framework, we demonstrate that
multicalibration error exhibits dependence on the classifier architecture as
well as the underlying data distribution. We perform an experimental evaluation
to investigate the behavior of multicalibration error for different families of
classifiers. We compare the results of this evaluation to multicalibration
error concentration bounds. Our investigation provides additional perspective
on both algorithmic fairness and multicalibration error convergence bounds.
Given the prevalence of ERM sample complexity bounds, our proposed framework
enables machine learning practitioners to easily understand the convergence
behavior of multicalibration error for a myriad of classifier architectures.
