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Abstract:
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The problem is motivated by eQTL studies in genomic research, whose goal is to identify genetic variations that may affect expressions of certain set of genes. The task can be viewed as a multivariate regression problem with variable selection on both responses (gene expression) and covariates (genetic variations), including also multi-way interactions among covariates. Instead of learning a predictive model of quantitative trait given combinations of genetic markers, we propose to to partition the $y$'s and the $x$'s simultaneously, and use a logistic or probit function to link a cluster of $y$'s to a cluster of $x$'s so as to achieve the variable selection task.
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