Structured sparse canonical correlation analysis

In this paper, we propose to apply sparse canonical correlation analysis (sparse CCA) to an important genome-wide association study problem, eQTL mapping. Existing sparse CCA models do not incorporate structural information among variables such as pathways of genes. This work extends the sparse CCA so that it could exploit either the pre-given or unknown group structure via the structured-sparsity-inducing penalty. Such structured penalty poses new challenge on optimization techniques. To address this challenge, by specializing the excessive gap framework, we develop a scalable primal-dual optimization algorithm with a fast rate of convergence. Empirical results show that the proposed optimization algorithm is more efficient than existing state-of-the-art methods. We also demonstrate the effectiveness of the structured sparse CCA on both simulated and genetic datasets.