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

VAEs in the Presence of Missing Data