  This work includes a number of novel contributions for the multiple-source
adaptation problem. We present new normalized solutions with strong theoretical
guarantees for the cross-entropy loss and other similar losses. We also provide
new guarantees that hold in the case where the conditional probabilities for
the source domains are distinct. Moreover, we give new algorithms for
determining the distribution-weighted combination solution for the
cross-entropy loss and other losses. We report the results of a series of
experiments with real-world datasets. We find that our algorithm outperforms
competing approaches by producing a single robust model that performs well on
any target mixture distribution. Altogether, our theory, algorithms, and
empirical results provide a full solution for the multiple-source adaptation
problem with very practical benefits.
