  Ensembles depend on diversity for improved performance. Many ensemble
training methods, therefore, attempt to optimize for diversity, which they
almost always define in terms of differences in training set predictions. In
this paper, however, we demonstrate the diversity of predictions on the
training set does not necessarily imply diversity under mild covariate shift,
which can harm generalization in practical settings. To address this issue, we
introduce a new diversity metric and associated method of training ensembles of
models that extrapolate differently on local patches of the data manifold.
Across a variety of synthetic and real-world tasks, we find that our method
improves generalization and diversity in qualitatively novel ways, especially
under data limits and covariate shift.
