  Rates of missing data often depend on record-keeping policies and thus may
change across times and locations, even when the underlying features are
comparatively stable. In this paper, we introduce the problem of Domain
Adaptation under Missingness Shift (DAMS). Here, (labeled) source data and
(unlabeled) target data would be exchangeable but for different missing data
mechanisms. We show that if missing data indicators are available, DAMS reduces
to covariate shift. Addressing cases where such indicators are absent, we
establish the following theoretical results for underreporting completely at
random: (i) covariate shift is violated (adaptation is required); (ii) the
optimal linear source predictor can perform arbitrarily worse on the target
domain than always predicting the mean; (iii) the optimal target predictor can
be identified, even when the missingness rates themselves are not; and (iv) for
linear models, a simple analytic adjustment yields consistent estimates of the
optimal target parameters. In experiments on synthetic and semi-synthetic data,
we demonstrate the promise of our methods when assumptions hold. Finally, we
discuss a rich family of future extensions.
