Abstract
Multi-omics characterization of single cells holds outstanding potential for profiling the dynamics and relations of gene regulatory states of thousands of cells. How to integrate multimodal data is an open problem, especially when aiming to combine data from multiple sources or conditions containing both biological and technical variation. We introduce liam, a flexible model for the simultaneous horizontal and vertical integration of paired single-cell multimodal data and mosaic integration of paired with unimodal data. Liam learns a joint low-dimensional representation of the measured modalities, which proves beneficial when the information content or quality of the modalities differ. Its integration accounts for complex batch effects using a tunable combination of conditional and adversarial training, which can be optimized using replicate information while retaining selected biological variation. We demonstrate liam's superior performance on multiple paired multimodal data types, including Multiome and CITE-seq data, and in mosaic integration scenarios. Our detailed benchmarking experiments illustrate the complexities and challenges remaining for integration and the meaningful assessment of its success.