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Abstract:
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Variable selection procedures in regression models have been considered in various high-dimensional problems. However, most models assume that each individual observation is affected by the same set of predictor variables, and this assumption might not be flexible enough to catch some individual effect between predictors and the response. For example, senior patients may have a different set of genetic and demographic predictors associated with cancer status, compared to young patients. In this article, we propose a novel procedure to identify this heterogeneous sparsity patterns. We show that the proposed model selection procedure is consistent when the number of predictors tends to infinity. A wide range of simulation and real data analyses are provided, and the results show that the proposed procedure is successful in finding the individualized effect on variable selection. Moreover, when the true model is a traditional linear model, the procedure comparably performs compared to standard Bayesian variable selection methods.
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