A penalized regression model for the joint estimation of eQTL associations and gene network structure

Abstract

In this work, we present a new approach for jointly performing eQTL mapping and gene network inference while encouraging a transfer of information between the two tasks. We address this problem by formulating it as a multiple-output regression task in which we aim to learn the regression coefficients while simultaneously estimating the conditional independence relationships among the set of response variables. The approach we develop uses structured sparsity penalties to encourage the sharing of information between the regression coefficients and the output network in a mutually beneficial way. Our model, inverse-covariance-fused lasso, is formulated as a biconvex optimization problem that we solve via alternating minimization. We derive new, efficient optimization routines to solve each convex sub-problem that are based on extensions of state-of-the-art methods. Experiments on both simulated data and a yeast eQTL dataset demonstrate that our approach outperforms a large number of existing methods on the recovery of the true sparse structure of both the eQTL associations and the gene network. We also apply our method to a human Alzheimer’s disease dataset and highlight some results that support previous discoveries about the disease.