  Multi-source domain adaptation (DA) aims at leveraging information from more
than one source domain to make predictions in a target domain, where different
domains may have different data distributions. Most existing methods for
multi-source DA focus on classification problems while there is only limited
investigation in the regression settings. In this paper, we fill in this gap
through a two-step procedure. First, we extend a flexible single-source DA
algorithm for classification through outcome-coarsening to enable its
application to regression problems. We then augment our single-source DA
algorithm for regression with ensemble learning to achieve multi-source DA. We
consider three learning paradigms in the ensemble algorithm, which combines
linearly the target-adapted learners trained with each source domain: (i) a
multi-source stacking algorithm to obtain the ensemble weights; (ii) a
similarity-based weighting where the weights reflect the quality of DA of each
target-adapted learner; and (iii) a combination of the stacking and similarity
weights. We illustrate the performance of our algorithms with simulations and a
data application where the goal is to predict High-density lipoprotein (HDL)
cholesterol levels using gut microbiome. We observe a consistent improvement in
prediction performance of our multi-source DA algorithm over the routinely used
methods in all these scenarios.
