  Real world datasets often contain entries with missing elements e.g. in a
medical dataset, a patient is unlikely to have taken all possible diagnostic
tests. Variational Autoencoders (VAEs) are popular generative models often used
for unsupervised learning. Despite their widespread use it is unclear how best
to apply VAEs to datasets with missing data. We develop a novel latent variable
model of a corruption process which generates missing data, and derive a
corresponding tractable evidence lower bound (ELBO). Our model is
straightforward to implement, can handle both missing completely at random
(MCAR) and missing not at random (MNAR) data, scales to high dimensional inputs
and gives both the VAE encoder and decoder principled access to indicator
variables for whether a data element is missing or not. On the MNIST and SVHN
datasets we demonstrate improved marginal log-likelihood of observed data and
better missing data imputation, compared to existing approaches.
