The Missing Indicator Method: From Low to High Dimensions
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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 work only on complete data, thus requiring preprocessing, such as missing value imputation, to work on incomplete data sets. However, imputation discards potentially useful information encoded by the pattern of missing values. 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. We show experimentally that MIM improves performance for informative missing values, and we prove that MIM does not hurt linear models asymptotically for uninformative missing values. Nonetheless, MIM can increase variance if many of the added indicators are uninformative, causing harm particularly for high-dimensional data sets. To address this issue, we introduce Selective MIM (SMIM), a method that adds missing indicators only for features that have informative missing patterns. We show empirically that SMIM performs at least as well as MIM across a range of experimental settings, and improves MIM for high-dimensional data.
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