With the aim of building machine learning systems that incorporate standards of fairness and accountability, we explore explicit subgroup sample complexity bounds. The work is motivated by the observation that classifier predictions for real world datasets often demonstrate drastically different metrics, such as accuracy, when subdivided by specific sensitive variable subgroups. The reasons for these discrepancies are varied and not limited to the influence of mitigating variables, institutional bias, underlying population distributions as well as sampling bias. Among the numerous definitions of fairness that exist, we argue that at a minimum, principled ML practices should ensure that classification predictions are able to mirror the underlying sub-population distributions. However, as the number of sensitive variables increase, populations meeting at the intersectionality of these variables may simply not exist or may not be large enough to provide accurate samples for classification. In these increasingly likely scenarios, we make the case for human intervention and applying situational and individual definitions of fairness. In this paper we present lower bounds of subgroup sample complexity for metric-fair learning based on the theory of Probably Approximately Metric Fair Learning. We demonstrate that for a classifier to approach a definition of fairness in terms of specific sensitive variables, adequate subgroup population samples need to exist and the model dimensionality has to be aligned with subgroup population distributions. In cases where this is not feasible, we propose an approach using individual fairness definitions for achieving alignment. We look at two commonly explored UCI datasets under this lens and suggest human interventions for data collection for specific subgroups to achieve approximate individual fairness for linear hypotheses.
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