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

Fairness Sample Complexity and the Case for Human Intervention