Recent advances in single-cell technologies enable joint profiling of multiple omics. These profiles can reveal the complex interplay of different regulatory layers in single cells; still, new challenges arise when integrating datasets with some features shared across experiments and others exclusive to a single source; combining information across these sources is called mosaic integration. The difficulties lie in imputing missing molecular layers to build a self-consistent atlas, finding a common latent space, and transferring learning to new data sources robustly. Existing mosaic integration approaches based on matrix factorization cannot efficiently adapt to nonlinear embeddings for the latent cell space and are not designed for accurate imputation of missing molecular layers. By contrast, we propose a probabilistic variational autoencoder model, scVAEIT, to integrate and impute multimodal datasets with mosaic measurements. A key advance is the use of a missing mask for learning the conditional distribution of unobserved modalities and features, which makes scVAEIT flexible to combine different panels of measurements from multimodal datasets accurately and in an end-to-end manner. Imputing the masked features serves as a supervised learning procedure while preventing overfitting by regularization. Focusing on gene expression, protein abundance, and chromatin accessibility, we validate that scVAEIT robustly imputes the missing modalities and features of cells biologically different from the training data. scVAEIT also adjusts for batch effects while maintaining the biological variation, which provides better latent representations for the integrated datasets. We demonstrate that scVAEIT significantly improves integration and imputation across unseen cell types, different technologies, and different tissues.

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