*Result*: A technical review of multi-omics data integration methods: from classical statistical to deep generative approaches.

*The rapid advancement of high-throughput sequencing and other assay technologies has resulted in the generation of large and complex multi-omics datasets, offering unprecedented opportunities for advancing precision medicine. However, multi-omics data integration remains challenging due to the high-dimensionality, heterogeneity, and frequency of missing values across data types. Computational methods leveraging statistical and machine learning approaches have been developed to address these issues and uncover complex biological patterns, improving our understanding of disease mechanisms. Here, we comprehensively review state-of-the-art multi-omics integration methods with a focus on deep generative models, particularly variational autoencoders (VAEs) that have been widely used for data imputation, augmentation, and batch effect correction. We explore the technical aspects of VAE loss functions and regularisation techniques, including adversarial training, disentanglement, and contrastive learning. Moreover, we highlight recent advancements in foundation models and multimodal data integration, outlining future directions in precision medicine research. [ABSTRACT FROM AUTHOR]

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