  Learning low-dimensional representations of single-cell transcriptomics has
become instrumental to its downstream analysis. The state of the art is
currently represented by neural network models such as variational autoencoders
(VAEs) which use a variational approximation of the likelihood for inference.
We here present the Deep Generative Decoder (DGD), a simple generative model
that computes model parameters and representations directly via maximum a
posteriori (MAP) estimation. The DGD handles complex parameterized latent
distributions naturally unlike VAEs which typically use a fixed Gaussian
distribution, because of the complexity of adding other types. We first show
its general functionality on a commonly used benchmark set, Fashion-MNIST.
Secondly, we apply the model to multiple single-cell data sets. Here the DGD
learns low-dimensional, meaningful and well-structured latent representations
with sub-clustering beyond the provided labels. The advantages of this approach
are its simplicity and its capability to provide representations of much
smaller dimensionality than a comparable VAE.
