  Recent years have witnessed a great success of supervised deep learning,
where predictive models were trained from a large amount of fully labeled data.
However, in practice, labeling such big data can be very costly and may not
even be possible for privacy reasons. Therefore, in this paper, we aim to learn
an accurate classifier without any class labels. More specifically, we consider
the case where multiple sets of unlabeled data and only their class priors,
i.e., the proportions of each class, are available. Under this problem setup,
we first derive an unbiased estimator of the classification risk that can be
estimated from the given unlabeled sets and theoretically analyze the
generalization error of the learned classifier. We then find that the
classifier obtained as such tends to cause overfitting as its empirical risks
go negative during training. To prevent overfitting, we further propose a
partial risk regularization that maintains the partial risks with respect to
unlabeled datasets and classes to certain levels. Experiments demonstrate that
our method effectively mitigates overfitting and outperforms state-of-the-art
methods for learning from multiple unlabeled sets.
