Efficient and Multiply Robust Risk Estimation under General Forms of Dataset Shift
Statistical machine learning methods often face the challenge of limited data
available from the population of interest. One remedy is to leverage data from
auxiliary source populations, which share some conditional distributions or are
linked in other ways with the target domain. Techniques leveraging such
\emph{dataset shift} conditions are known as \emph{domain adaptation} or
\emph{transfer learning}. Despite extensive literature on dataset shift,
limited works address how to efficiently use the auxiliary populations to
improve the accuracy of risk evaluation for a given machine learning task in
the target population.
  In this paper, we study the general problem of efficiently estimating target
population risk under various dataset shift conditions, leveraging
semiparametric efficiency theory. We consider a general class of dataset shift
conditions, which includes three popular conditions -- covariate, label and
concept shift -- as special cases. We allow for partially non-overlapping
support between the source and target populations. We develop efficient and
multiply robust estimators along with a straightforward specification test of
these dataset shift conditions. We also derive efficiency bounds for two other
dataset shift conditions, posterior drift and location-scale shift. Simulation
studies support the efficiency gains due to leveraging plausible dataset shift
conditions.