Learning interpretable representations of single-cell multi-omics data with multi-output Gaussian Processes

Learning representations of single-cell genomics data is challenging due to the non-linear and often multi-modal nature of the data on one hand and the need for interpretable representations on the other hand. Existing approaches tend to either focus on interpretability aspects via linear matrix factorisation or on maximising expressive power via neural-network based embeddings using black-box variational autoencoders or graph embedding approaches. We address this trade-off between expressive power and interpretability by introducing a novel approach that combines highly expressive representation learning via an embedding layer with an interpretable multi-output Gaussian processes within a unified framework. In our model, we learn distinct representations for samples (cells) and features (genes) from multi-modal single-cell data. We demonstrate that even a few interpretable latent dimensions can effectively capture the underlying structure of the data. Our model yields interpretable relationships between groups of cells and their associated marker genes: leveraging a gene relevance map, we establish connections between cell clusters (e.g. specific cell types) and feature clusters (e.g., marker genes for those specific cell types) within the learnt latent spaces of cells and features.