Gharib, ShayanShayanGharibMurena, Pierre-AlexandrePierre-AlexandreMurenaKlami, ArtoArtoKlami2025-10-072025-10-072025-09-08Transactions on machine learning research (in Press): (2025)https://hdl.handle.net/11420/57831We study learning a multi-label classifier from partially labeled data, where each instance has only a single positive label. We explain how auxiliary information available on the label cardinality, the number of positive labels per instance, can be used for improving such methods. We consider auxiliary information of varying granularity, ranging from knowing just the maximum number of labels over all instances to knowledge on the distribution of label cardinalities and even the exact cardinality of each instance. We introduce methods leveraging the different types of auxiliary information, study how close to the fully labeled accuracy we can get under different scenarios, and show that an easy-to-implement method only assuming the knowledge of the maximum cardinality is comparable to the state-ofthe-art single-positive multi-label learning methods when using the same base model. Our implementation is publicly available at https://github.com/shayangharib/SPMLL_with_Label_Cardinality.en2835-88562025OpenReview.nethttps://creativecommons.org/licenses/by/4.0/Computer Science, Information and General Works::006: Special computer methodsNatural Sciences and Mathematics::519: Applied Mathematics, ProbabilitiesJournal Articlehttps://doi.org/10.15480/882.1595710.15480/882.15957Journal Article