  Data with missing values is ubiquitous in many applications. Recent years
have witnessed increasing attention on prediction with only incomplete data
consisting of observed features and a mask that indicates the missing pattern.
Existing methods assume that the training and testing distributions are the
same, which may be violated in real-world scenarios. In this paper, we consider
prediction with incomplete data in the presence of distribution shift. We focus
on the case where the underlying joint distribution of complete features and
label is invariant, but the missing pattern, i.e., mask distribution may shift
agnostically between training and testing. To achieve generalization, we
leverage the observation that for each mask, there is an invariant optimal
predictor. To avoid the exponential explosion when learning them separately, we
approximate the optimal predictors jointly using a double parameterization
technique. This has the undesirable side effect of allowing the learned
predictors to rely on the intra-mask correlation and that between features and
mask. We perform decorrelation to minimize this effect. Combining the
techniques above, we propose a novel prediction method called StableMiss.
Extensive experiments on both synthetic and real-world datasets show that
StableMiss is robust and outperforms state-of-the-art methods under agnostic
mask distribution shift.
