  We propose a probabilistic model for interpreting gene expression levels that
are observed through single-cell RNA sequencing. In the model, each cell has a
low-dimensional latent representation. Additional latent variables account for
technical effects that may erroneously set some observations of gene expression
levels to zero. Conditional distributions are specified by neural networks,
giving the proposed model enough flexibility to fit the data well. We use
variational inference and stochastic optimization to approximate the posterior
distribution. The inference procedure scales to over one million cells, whereas
competing algorithms do not. Even for smaller datasets, for several tasks, the
proposed procedure outperforms state-of-the-art methods like ZIFA and
ZINB-WaVE. We also extend our framework to account for batch effects and other
confounding factors, and propose a Bayesian hypothesis test for differential
expression that outperforms DESeq2.
