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We consider semi-supervised binary classification for applications in whichdata points are naturally grouped (e.g., survey responses grouped by state) andthe labeled data is biased (e.g., survey respondents are not representative ofthe population). The groups overlap in the feature space and consequently theinput-output patterns are related across the groups. To model the inherentstructure in such data, we assume the partition-projected class-conditionalinvariance across groups, defined in terms of the group-agnostic feature space.We demonstrate that under this assumption, the group carries additionalinformation about the class, over the group-agnostic features, with provablyimproved area under the ROC curve. Further assuming invariance ofpartition-projected class-conditional distributions across both labeled andunlabeled data, we derive a semi-supervised algorithm that explicitly leveragesthe structure to learn an optimal, group-aware, probability-calibratedclassifier, despite the bias in the labeled data. Experiments on synthetic andreal data demonstrate the efficacy of our algorithm over suitable baselines andablative models, spanning standard supervised and semi-supervised learningapproaches, with and without incorporating the group directly as a feature.

Leveraging Structure for Improved Classification of Grouped Biased Data