  In conventional supervised classification, true labels are required for
individual instances. However, it could be prohibitive to collect the true
labels for individual instances, due to privacy concerns or unaffordable
annotation costs. This motivates the study on classification from aggregate
observations (CFAO), where the supervision is provided to groups of instances,
instead of individual instances. CFAO is a generalized learning framework that
contains various learning problems, such as multiple-instance learning and
learning from label proportions. The goal of this paper is to present a novel
universal method of CFAO, which holds an unbiased estimator of the
classification risk for arbitrary losses -- previous research failed to achieve
this goal. Practically, our method works by weighing the importance of each
label for each instance in the group, which provides purified supervision for
the classifier to learn. Theoretically, our proposed method not only guarantees
the risk consistency due to the unbiased risk estimator but also can be
compatible with arbitrary losses. Extensive experiments on various problems of
CFAO demonstrate the superiority of our proposed method.
