In methylome-wide association studies (MWAS) there are many possible differences between cases and controls (e.g. related to life style, diet, and medication use) that may affect the methylome and produce false positive findings. An effective approach to control for these confounders is to first capture the major sources of variation in the methylation data and then regress out these components in the association analyses. This approach is, however, computationally very challenging due to the extremely large number of methylation sites in the human genome.