Outline of the structure of Step 2 of the algorithm.

<p>(a) After selection of phenotypes in Step 1, we produce a covariance matrix between observed gene expression products, and their associated unique <i>cis</i>-eQTL. (b) A convex feature selection method (the adaptive lasso) is used to learn the structure of the inverse covariance matrix, which is also the conditional independence or interaction network among gene expression products and <i>cis</i>-eQTL genotypes. (c) The directed cyclic network among expression products can then be recovered directly from the conditional independence network, using the “Recovery” Theorem. For Step 3, each of the induced edges between expression phenotypes and <i>cis</i>-eQTL, shown in (b), are tested to ensure marginal independence using a permutation test.