New variance-reduced bag-level losses bring the sample complexity of LLP under square loss down to k/β (realizable) and k/β² (non-realizable), with a lower bound showing linear dependence on bag size is necessary.
Deep learning from label proportions for emphysema quantification
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Nearly Optimal Sample Complexity for Learning with Label Proportions
New variance-reduced bag-level losses bring the sample complexity of LLP under square loss down to k/β (realizable) and k/β² (non-realizable), with a lower bound showing linear dependence on bag size is necessary.