Leveraging input and output structures for joint mapping of epistatic and marginal eQTLs

Motivation: As many complex disease and expression phenotypes are the outcome of intricate perturbation of molecular networks underlying gene regulation resulted from interdependent genome variations, association mapping of causal QTLs or expression quantitative trait loci must consider both additive and epistatic effects of multiple candidate genotypes. This problem poses a significant challenge to contemporary genome-wide-association (GWA) mapping technologies because of its computational complexity. Fortunately, a plethora of recent developments in biological network community, especially the availability of genetic interaction networks, make it possible to construct informative priors of complex interactions between genotypes, which can substantially reduce the complexity and increase the statistical power of GWA inference. Results: In this article, we consider the problem of learning a multitask regression model while taking advantage of the prior information on structures on both the inputs (genetic variations) and outputs (expression levels). We propose a novel regularization scheme over multitask regression called jointly structured input–output lasso based on an ℓ(1)/ℓ(2) norm, which allows shared sparsity patterns for related inputs and outputs to be optimally estimated. Such patterns capture multiple related single nucleotide polymorphisms (SNPs) that jointly influence multiple-related expression traits. In addition, we generalize this new multitask regression to structurally regularized polynomial regression to detect epistatic interactions with manageable complexity by exploiting the prior knowledge on candidate SNPs for epistatic effects from biological experiments. We demonstrate our method on simulated and yeast eQTL datasets. Availability: Software is available at http://www.sailing.cs.cmu.edu/. Contact: epxing@cs.cmu.edu