  Learning from Label Proportions (LLP) is a weakly supervised learning method
that aims to perform instance classification from training data consisting of
pairs of bags containing multiple instances and the class label proportions
within the bags. Previous studies on multiclass LLP can be divided into two
categories according to the learning task: per-instance label classification
and per-bag label proportion estimation. However, these methods often results
in high variance estimates of the risk when applied to complex models, or lack
statistical learning theory arguments. To address this issue, we propose new
learning methods based on statistical learning theory for both per-instance and
per-bag policies. We demonstrate that the proposed methods are respectively
risk-consistent and classifier-consistent in an instance-wise manner, and
analyze the estimation error bounds. Additionally, we present a heuristic
approximation method that utilizes an existing method for regressing label
proportions to reduce the computational complexity of the proposed methods.
Through benchmark experiments, we demonstrated the effectiveness of the
proposed methods.
