When training predictive models on data with missing entries, the most widely
used and versatile approach is a pipeline technique where we first impute
missing entries and then compute predictions. In this paper, we view prediction
with missing data as a two-stage adaptive optimization problem and propose a
new class of models, adaptive linear regression models, where the regression
coefficients adapt to the set of observed features. We show that some adaptive
linear regression models are equivalent to learning an imputation rule and a
downstream linear regression model simultaneously instead of sequentially. We
leverage this joint-impute-then-regress interpretation to generalize our
framework to non-linear models. In settings where data is strongly not missing
at random, our methods achieve a 2-10% improvement in out-of-sample accuracy.

训练具有缺失条目的预测模型时，我们可以利用两阶段自适应优化问题来处理缺失数据，并提出了一种新类模型，即自适应线性回归模型，其中回归系数根据观测特征进行自适应。我们展示了一些自适应线性回归模型等价于同时学习一个填充规则和一个下游线性回归模型，而不是顺序学习。我们利用这种联合填充 - 回归解释来推广我们的框架到非线性模型。在数据不随机缺失的情况下，我们的方法可以提高 2-10% 的样本外准确率。