One of the most commonly used approaches in the joint integrative analysis omics data measured on the same samples, such as SNP and gene expression data (eQTL), or proteomic and transcriptomic data, is classical canonical correlation analysis (CCA), or some modern variation of it (e.g. sparse CCA). In addition, related methods such as O2PLS or the RV coefficient to measure and dissect total association between groups of variables, that have been developed and are widely used in chemometrics are now also been used in the analysis of omics data. Unfortunately, despite their widespread use a major drawback of these projective methods is the lack of interpretability of the latent variables, and in the case of the RV coefficient, incoherency.
Here we present a simple alternative approach to integrative genomics based on using relative entropy to characterize the overall association between two (or more) sets of omic data. This approach is natural in the setting of latent-variable multivariate regression and we show that in case of normal variables this measure offers a canonical decomposition that allows to infer the underlying corresponding association network among the individual covariates. Furthermore, the approach is computationally inexpensive and can be applied to large-dimensional data sets, and can be easily applied to two or more groups of variables based on optimal whitening of the individual data sets. We illustrate this approach by analyzing metabolomic and transcriptomic data.