In this paper, we address the segmentation of tumor subtypes in whole slide
images (WSI) by utilizing incomplete label proportions. Specifically, we
utilize `partial' label proportions, which give the proportions among tumor
subtypes but do not give the proportion between tumor and non-tumor. Partial
label proportions are recorded as the standard diagnostic information by
pathologists, and we, therefore, want to use them for realizing the
segmentation model that can classify each WSI patch into one of the tumor
subtypes or non-tumor. We call this problem ``learning from partial label
proportions (LPLP)'' and formulate the problem as a weakly supervised learning
problem. Then, we propose an efficient algorithm for this challenging problem
by decomposing it into two weakly supervised learning subproblems: multiple
instance learning (MIL) and learning from label proportions (LLP). These
subproblems are optimized efficiently in the end-to-end manner. The
effectiveness of our algorithm is demonstrated through experiments conducted on
two WSI datasets.

本文通过利用不完全的标签比例解决了整个切片图像中肿瘤亚型的分割问题，提出了一个高效的算法将其分解为两个弱监督学习子问题：多实例学习和从标签比例中学习，从而有效地进行优化。该算法在两个整个切片图像数据集上经过实验证明了其有效性。