  Latent variable models can be used to probabilistically "fill-in" missing
data entries. The variational autoencoder architecture (Kingma and Welling,
2014; Rezende et al., 2014) includes a "recognition" or "encoder" network that
infers the latent variables given the data variables. However, it is not clear
how to handle missing data variables in this network. The factor analysis (FA)
model is a basic autoencoder, using linear encoder and decoder networks. We
show how to calculate exactly the latent posterior distribution for the factor
analysis (FA) model in the presence of missing data, and note that this
solution implies that a different encoder network is required for each pattern
of missingness. We also discuss various approximations to the exact solution.
Experiments compare the effectiveness of various approaches to filling in the
missing data.
