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

Autoencoders and Probabilistic Inference with Missing Data: An Exact Solution for The Factor Analysis Case