  Learning from label proportions (LLP) is a weakly supervised classification
problem where data points are grouped into bags, and the label proportions
within each bag are observed instead of the instance-level labels. The task is
to learn a classifier to predict the individual labels of future individual
instances. Prior work on LLP for multi-class data has yet to develop a
theoretically grounded algorithm. In this work, we provide a theoretically
grounded approach to LLP based on a reduction to learning with label noise,
using the forward correction (FC) loss of \citet{Patrini2017MakingDN}. We
establish an excess risk bound and generalization error analysis for our
approach, while also extending the theory of the FC loss which may be of
independent interest. Our approach demonstrates improved empirical performance
in deep learning scenarios across multiple datasets and architectures, compared
to the leading existing methods.
