Fig. 6From: PCA outperforms popular hidden variable inference methods for molecular QTL mappingPCA, SVA, PEER, and HCP are closely related statistical methods despite their apparent dissimilarities. In particular, the methodology behind SVA, PEER, and HCP can all be traced back to PCA. PCA [34,35,36,37,38] is traditionally derived by optimizing some objective functions (either maximum variance or minimum reconstruction error; Additional file 1: Section S5.1), but more recently, it is shown that PCA can be derived as a limiting case of probabilistic principal component analysis (PPCA) [45], which in turn is a special case of factor analysis [35, 46]. PEER [24, 32] is based on a Bayesian probabilistic model and can be considered a Bayesian version of factor analysis. SVA [25, 26] is purely algorithmic and is not defined based on a probabilistic model or objective function. The steps of the SVA algorithm are complicated [44], but in a nutshell, SVA iterates between two steps: (1) reweight the features of the molecular phenotype matrix, and (2) perform PCA on the resulting matrix (with centering but without scaling) [26]. Lastly, HCP [33] is defined by minimizing a loss function that is very similar to the minimum-reconstruction-error loss function of PCA (Additional file 1: Section S5.2)Back to article page