Theoretical Proportion Label Perturbation for Learning from Label Proportions in Large Bags

Learning from label proportions (LLP) is a kind of weakly supervised learning that trains an instance-level classifier from label proportions of bags, which consist of sets of instances without using instance labels. A challenge in LLP arises when the number of instances in a bag (bag size) is numerous, making the traditional LLP methods difficult due to GPU memory limitations. This study aims to develop an LLP method capable of learning from bags with large sizes. In our method, smaller bags (mini-bags) are generated by sampling instances from large-sized bags (original bags), and these mini-bags are used in place of the original bags. However, the proportion of a mini-bag is unknown and differs from that of the original bag, leading to overfitting. To address this issue, we propose a perturbation method for the proportion labels of sampled mini-bags to mitigate overfitting to noisy label proportions. This perturbation is added based on the multivariate hypergeometric distribution, which is statistically modeled. Additionally, loss weighting is implemented to reduce the negative impact of proportions sampled from the tail of the distribution. Experimental results demonstrate that the proportion label perturbation and loss weighting achieve classification accuracy comparable to that obtained without sampling. Our codes are available at https://github.com/stainlessnight/LLP-LargeBags.