In this paper, we propose a novel sparse regression method for Brain-Wide and Genome-Wide association study. Specifically, we impose a low-rank constraint on the weight coefficient matrix and then decompose it into two low-rank matrices, which find relationships in genetic features and in brain imaging features, respectively. We also introduce a sparse acyclic digraph with sparsity-inducing penalty to take further into account the correlations among the genetic variables, by which it can be possible to identify the representative SNPs that are highly associated with the brain imaging features. We optimize our objective function by jointly tackling low-rank regression and variable selection in a framework. In our method, the low-rank constraint allows us to conduct variable selection with the low-rank representations of the data; the learned low-sparsity weight coefficients allow discarding unimportant variables at the end. The experimental results on the Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset showed that the proposed method could select the important SNPs to more accurately estimate the brain imaging features than the state-of-the-art methods.
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