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Abstract

The availability of the genetic background of large sample groups motivates genome-wide association studies which map the phenome of the sample to various genetic loci. A multitude of complex, high-dimensional phenotypes, like physiological measurements, cannot be treated as independent entities. Instead, pleiotropy, i.e. single genetic loci influencing large sets of phenotypes, calls for methods that account for interdependencies of the phenotypic traits. We address this important challenge using multi-task learning, providing a systematic framework to exploit the correlation structure of the phenome. Our method is scalable, allows large numbers of putative regulators and phenotypes to be modeled in a joint fashion. Here, Y is a phenotype matrix of N individuals \(\times\) K phenotypes, X is a genotype matrix of N individuals \(\times\) M SNPs, \& is a M\(\times\)K matrix that assigns phenotype-specific weights to SNPs and \% is a K \(\times\) K matrix combining the
predictions of correlated phenotypes. To ensure interpretability of the solutions, we employ a transparent sparsity prior, regularizing the weights \& on a per SNP level. This choice of regularization encourages sparse relations to SNPs while sharing information across correlated phenotypes. Methodologically, our approach advances the state-of-the-art [Kim+09] by jointly modeling of the correlation structure of the phenome and the relationships between SNPs and phenotypes. This leads to an optimization problem that is not jointly convex; however, can be efficiently tackled using an alternating procedure.},