VAEs in the Presence of Missing Data
This addresses a practical issue for users of VAEs in fields like medical data analysis where missing data is common, though it is an incremental improvement over existing approaches.
The paper tackles the problem of applying Variational Autoencoders (VAEs) to datasets with missing data by developing a novel latent variable model of a corruption process, resulting in improved marginal log-likelihood and better imputation on MNIST and SVHN datasets compared to existing methods.
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.