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 expres-sion levels. This can be viewed as a variable selection problem, potentially with high dimensionality. Variable selection is especially challenging in high dimensional set-tings, where it is difficult to detect subtle individual effects and interactions between factors. Bayesian additive regression trees (BART, Chipman et al., 2010) provides a novel nonparametric alternative to parametric regression approaches, such as the lasso or stepwise regression, especially when the number of relevant predictors is sparse rel-ative to the total number of available predictors 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 fur-ther, we adapt the BART procedure to incorporate informed prior information about variable importance. We present simulations demonstrating that our method com-pares favorably to existing parametric and nonparametric procedures in a variety of data settings. 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 (Saccha-romyces 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