  Selective labels occur when label observations are subject to a
decision-making process; e.g., diagnoses that depend on the administration of
laboratory tests. We study a clinically-inspired selective label problem called
disparate censorship, where labeling biases vary across subgroups and unlabeled
individuals are imputed as "negative" (i.e., no diagnostic test = no illness).
Machine learning models naively trained on such labels could amplify labeling
bias. Inspired by causal models of selective labels, we propose Disparate
Censorship Expectation-Maximization (DCEM), an algorithm for learning in the
presence of disparate censorship. We theoretically analyze how DCEM mitigates
the effects of disparate censorship on model performance. We validate DCEM on
synthetic data, showing that it improves bias mitigation (area between ROC
curves) without sacrificing discriminative performance (AUC) compared to
baselines. We achieve similar results in a sepsis classification task using
clinical data.
