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Multi-omics datasets are becoming more common, necessitating better integration methods to realize their revolutionary potential. Here, we introduce multi-set correlation and factor analysis (MCFA), an unsupervised integration method tailored to the unique challenges of high-dimensional genomics data that enables fast inference of shared and private factors. We used MCFA to integrate methylation markers, protein expression, RNA expression, and metabolite levels in 614 diverse samples from the Trans-Omics for Precision Medicine/Multi-Ethnic Study of Atherosclerosis multi-omics pilot. Samples cluster strongly by ancestry in the shared space, even in the absence of genetic information, while private spaces frequently capture dataset-specific technical variation. Finally, we integrated genetic data by conducting a genome-wide association study (GWAS) of our inferred factors, observing that several factors are enriched for GWAS hits and -expression quantitative trait loci. Two of these factors appear to be related to metabolic disease. Our study provides a foundation and framework for further integrative analysis of ever larger multi-modal genomic datasets.