  To cope with high annotation costs, training a classifier only from weakly
supervised data has attracted a great deal of attention these days. Among
various approaches, strengthening supervision from completely unsupervised
classification is a promising direction, which typically employs class priors
as the only supervision and trains a binary classifier from unlabeled (U)
datasets. While existing risk-consistent methods are theoretically grounded
with high flexibility, they can learn only from two U sets. In this paper, we
propose a new approach for binary classification from m U-sets for $m\ge2$. Our
key idea is to consider an auxiliary classification task called surrogate set
classification (SSC), which is aimed at predicting from which U set each
observed data is drawn. SSC can be solved by a standard (multi-class)
classification method, and we use the SSC solution to obtain the final binary
classifier through a certain linear-fractional transformation. We built our
method in a flexible and efficient end-to-end deep learning framework and prove
it to be classifier-consistent. Through experiments, we demonstrate the
superiority of our proposed method over state-of-the-art methods.
