  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.
