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 ).
