VARIABLE SELECTION FOR BART: AN APPLICATION TO GENE REGULATION

We consider the task of discovering gene regulatory networks, which are defined as sets of genes and the corresponding transcription factors which regulate their expression levels. This can be viewed as a variable selection problem, potentially with high dimensionality. Variable selection is espe-cially challenging in high-dimensional settings, where it is difficult to de-tect subtle individual effects and interactions between predictors. Bayesian Additive Regression Trees [BART, Ann. Appl. Stat. 4 (2010) 266–298] pro-vides a novel nonparametric alternative to parametric regression approaches, such as the lasso or stepwise regression, especially when the number of rel-evant predictors is sparse relative to the total number of available predic-tors and the fundamental relationships are nonlinear. We develop a principled permutation-based inferential approach for determining when the effect of a selected predictor is likely to be real. Going further, we adapt the BART pro-cedure to incorporate informed prior information about variable importance. We present simulations demonstrating that our method compares favorably to existing parametric and nonparametric procedures in a variety of data set-tings. To demonstrate the potential of our approach in a biological context, we apply it to the task of inferring the gene regulatory network in yeast (Sac-charomyces cerevisiae). We find that our BART-based procedure is best able to recover the subset of covariates with the largest signal compared to other variable selection methods. The methods developed in this work are readily available in the R package bartMachine. 1. Introduction. A