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Due to the high human cost of annotation, it is non-trivial to curate a large-scale medical dataset that is fully labeled for all classes of interest. Instead, it would be convenient to collect multiple small partially labeled datasets from different matching sources, where the medical images may have only been annotated for a subset of classes of interest. This paper offers an empirical understanding of an under-explored problem, namely partially supervised multi-label classification (PSMLC), where a multi-label classifier is trained with only partially labeled medical images. In contrast to the fully supervised counterpart, the partial supervision caused by medical data scarcity has non-trivial negative impacts on the model performance. A potential remedy could be augmenting the partial labels. Though vicinal risk minimization (VRM) has been a promising solution to improve the generalization ability of the model, its application to PSMLC remains an open question. To bridge the methodological gap, we provide the first VRM-based solution to PSMLC. The empirical results also provide insights into future research directions on partially supervised learning under data scarcity.