First provide a summary of the paper, and then address the following criteria: Quality, clarity, originality and significance. This paper addresses the problem of learning with label proportions, wherein one only knows the proportions of the labels of bags of samples that are positive (or more generally that belong to one class). It makes very substantive contributions by: a. analysis that shows that a general class of loss functions allow efficient learning via the mean operator without requiring homogeneity (as was the case with previous literature) b. Developing fast learning algorithms for estimating the mean operator c. allow the use of standard binary classifier learning algorithms to solve the LLP problem via reduction. It is also very well written, though it is quite dense because of the sheer volume of novel material that the authors try to cover in a short NIPS paper.