  We propose a variational autoencoder architecture to model both ignorable and
nonignorable missing data using pattern-set mixtures as proposed by Little
(1993). Our model explicitly learns to cluster the missing data into
missingness pattern sets based on the observed data and missingness masks.
Underpinning our approach is the assumption that the data distribution under
missingness is probabilistically semi-supervised by samples from the observed
data distribution. Our setup trades off the characteristics of ignorable and
nonignorable missingness and can thus be applied to data of both types. We
evaluate our method on a wide range of data sets with different types of
missingness and achieve state-of-the-art imputation performance. Our model
outperforms many common imputation algorithms, especially when the amount of
missing data is high and the missingness mechanism is nonignorable.
