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.

We introduce sentenceMIM, a probabilistic auto-encoder for language modelling, trained with Mutual Information Machine (MIM) learning. Previous attempts to learn variational auto-encoders for language data have had mixed success, with empirical performance well below state-of-the-art auto-regressive models, a key barrier being the occurrence of posterior collapse with VAEs. The recently proposed MIM framework encourages high mutual information between observations and latent variables, and is more robust against posterior collapse. This paper formulates a MIM model for text data, along with a corresponding learning algorithm. We demonstrate excellent perplexity (PPL) results on several datasets, and show that the framework learns a rich latent space, allowing for interpolation between sentences of different lengths with a fixed-dimensional latent representation. We also demonstrate the versatility of sentenceMIM by utilizing a trained model for question-answering, a transfer learning task, without fine-tuning. To the best of our knowledge, this is the first latent variable model (LVM) for text modelling that achieves competitive performance with non-LVM models.