Multiomics factor analysis (MOFA)

MOFA¹⁵ decomposes each omics into the product of a factor matrix and omics-specific weight matrices:

MOFA first formulates the equation above in a probabilistic Bayesian model, placing prior distributions on all unobserved variables Ai,FandEi. While the factor matrix F is shared across all omics, the sparsity priors in the in Aⁱ ensure that both omics-specific and shared factors are retrieved. MOFA solves the probabilistic Bayesian model by maximizing the Evidence Lower Bound (ELBO), which is equal to the sum of the model evidence and the negative Kullback–Leibler divergence between the true posterior and the variational distribution. Despite having a factor matrix Fshared among all omics, the sparsity priors in the weights ensure that MOFA will detect both omic-speciifc and shared factors. MOFA is an extension of Factor Analysis to multiomics data, but it is also partially related to iCluster. However, differently from iCluster, MOFA does not assume a normal distribution for the errors but supports combinations of different omics-specific error distributions. The code to run MOFA is available at https://github.com/bioFAM/MOFA. The MOFA package further implements an automatic downstream analysis pipeline for the interpretation of the obtained factor and weight matrices through pathways, top-contributing features or percentage of variance-explained interpretation.