On Characterizing and Mitigating Imbalances in Multi-Instance Partial Label Learning

Multi-Instance Partial Label Learning (MI-PLL) is a weakly-supervised learning setting encompassing partial label learning, latent structural learning, and neurosymbolic learning. Differently from supervised learning, in MI-PLL, the inputs to the classifiers at training-time are tuples of instances $\textbf{x}$, while the supervision signal is generated by a function $\sigma$ over the gold labels of $\textbf{x}$. The gold labels are hidden during training. In this paper, we focus on characterizing and mitigating learning imbalances, i.e., differences in the errors occurring when classifying instances of different classes (aka class-specific risks), under MI-PLL. The phenomenon of learning imbalances has been extensively studied in the context of long-tail learning; however, the nature of MI-PLL introduces new challenges. Our contributions are as follows. From a theoretical perspective, we characterize the learning imbalances by deriving class-specific risk bounds that depend upon the function $\sigma$. Our theory reveals that learning imbalances exist in MI-PLL even when the hidden labels are uniformly distributed. On the practical side, we introduce a technique for estimating the marginal of the hidden labels using only MI-PLL data. Then, we introduce algorithms that mitigate imbalances at training- and testing-time, by treating the marginal of the hidden labels as a constraint. The first algorithm relies on a novel linear programming formulation of MI-PLL for pseudo-labeling. The second one adjusts a model's scores based on robust optimal transport. We demonstrate the effectiveness of our techniques using strong neurosymbolic and long-tail learning baselines, discussing also open challenges.