Missing data is common in applied data science, particularly for tabular data sets found in healthcare, social sciences, and natural sciences. Most supervised learning methods only work on complete data, thus requiring preprocessing such as missing value imputation to work on incomplete data sets. However, imputation alone does not encode useful information about the missing values themselves. For data sets with informative missing patterns, the Missing Indicator Method (MIM), which adds indicator variables to indicate the missing pattern, can be used in conjunction with imputation to improve model performance. While commonly used in data science, MIM is surprisingly understudied from an empirical and especially theoretical perspective. In this paper, we show empirically and theoretically that MIM improves performance for informative missing values, and we prove that MIM does not hurt linear models asymptotically for uninformative missing values. Additionally, we find that for high-dimensional data sets with many uninformative indicators, MIM can induce model overfitting and thus test performance. To address this issue, we introduce Selective MIM (SMIM), a novel MIM extension that adds missing indicators only for features that have informative missing patterns. We show empirically that SMIM performs at least as well as MIM in general, and improves MIM for high-dimensional data. Lastly, to demonstrate the utility of MIM on real-world data science tasks, we demonstrate the effectiveness of MIM and SMIM on clinical tasks generated from the MIMIC-III database of electronic health records.

翻译：缺失数据在应用数据科学中普遍存在，尤其在医疗、社会科学和自然科学领域的表格数据集中。大多数监督学习方法仅适用于完整数据，因此需要对不完整数据集进行预处理，如缺失值插补。然而，仅进行插补并不能编码关于缺失值本身的有用信息。对于存在信息性缺失模式的数据集，缺失指示符方法（MIM）通过添加指示变量来标识缺失模式，可结合插补使用以提升模型性能。尽管MIM在数据科学中广泛使用，但令人惊讶的是，其经验性尤其是理论性研究尚不充分。本文通过实验和理论证明，MIM能提升信息性缺失值场景下的模型性能，并论证了在非信息性缺失值场景下，MIM渐近地不会损害线性模型。此外，我们发现对于包含大量非信息性指示符的高维数据集，MIM可能导致模型过拟合，进而影响测试性能。为解决此问题，我们提出选择性MIM（SMIM），这是一种新型MIM扩展方法，仅对具有信息性缺失模式的特征添加缺失指示符。实验表明，SMIM整体性能至少与MIM相当，并在高维数据上优于MIM。最后，为验证MIM在实际数据科学任务中的效用，我们基于MIMIC-III电子健康记录数据库生成的临床任务，展示了MIM和SMIM的有效性。