A stochastic partitioning method to associate high-dimensional responses and covariates

Abstract

We consider the problem of variable selection in data sets with many response variables and many covariates. A method is proposed that allows some covariates to affect some response variables and not others, and that clusters responses which have similar dependence on the same set of covariates. A Markov chain Monte Carlo procedure is employed to sample from the space of pairwise partitions of covariates and outcomes, where a pair consists of a subset of all outcomes and their associated covariates. We assess the performance of the method on simulated data and apply it to genomic data.