Fig. 1

siVAE infers interpretable representations of single-cell genomic data. a The input to siVAE is a cell-by-feature matrix; shown here is a synthetic gene expression matrix of eight genes, four of which are tightly regulated (genes 1–4), and the other four of which vary independently (genes 5–8). siVAE is a neural network consisting of a pair of encoder-decoders, that jointly learn a cell-embedding space and feature embedding space. The cell-wise encoder-decoder acts similarly to a canonical VAE, where the input to the encoder is a single cell c’s measurement across all input features (X_{c, :}). The cell-wise encoder uses the input cell measurements to compute an approximate posterior distribution over the location of the cell in the cell-embedding space. The feature-wise encoder-decoder takes as input measurements for a single feature f across all input training cells (X_{:, f}), and computes an approximate posterior distribution over the location of the feature in the feature embedding space. The decoders of the cell-wise and feature-wise encoder-decoders combine to output the expression level of feature f in cell c (X_{c, f}). b,d Visualization of the cell and feature embedding spaces learned from the gene expression matrix in a. Note in d that the embeddings of genes 1, 2, 3, and 4 all have large magnitudes along dimension 1 but not dimension 2, suggesting genes 1, 2, 3, and 4 explain variation in the cell-embedding space along dimension 1. Genes 5, 6, 7, and 8 are located at the origin of the feature embedding space, suggesting they do not co-vary with other features. c The expression patterns of gene 1 are overlaid on the cells in the cell-embedding space. Gene 1 clearly increases in expression when inspecting cells from left to right, consistent with the feature embedding space that shows Gene 1 having large loadings on dimension 1. e A trained siVAE model can be used to identify hubs and gene neighbors in a gene co-expression network, without the need to explicitly infer a co-expression network