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 especially challenging in high-dimensional settings, where it is difficult to detect subtle individual effects and interactions between predictors. Bayesian Additive Regression Trees [BART, Ann. Appl. Stat. 4 (2010) 266-298] 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 relative 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 further, we adapt the BART procedure 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 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 (Saccharomyces 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.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS755 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Is There Enhanced Depletion of Gas-Phase Nitrogen in Moderately Reddened Lines of Sight?

We report on the abundance of interstellar neutral nitrogen (NI) for 30 sightlines, using data from the Far Ultraviolet Spectroscopic Explorer (FUSE) and the Hubble Space Telescope (HST). NI column densities are derived by measuring the equivalent widths of several ultraviolet absorption lines and subsequently fitting those to a curve of growth. We find a mean interstellar N/H of 51+/-4 ppm. This is below the mean found by Meyer et al. of 62(+4,-3) ppm (adjusted for a difference in f-values). Our mean N/H is similar, however, to the (f-value adjusted) mean of 51+/-3 ppm found by Knauth et al. for a larger sample of sightlines with larger hydrogen column densities comparable to those in this study. We discuss the question of whether or not nitrogen shows increased gas-phase depletion in lines of sight with column densities log(H_tot) >~ 21, as claimed by Knauth et al. The nitrogen abundance in the line of sight toward HD 152236 is particularly interesting. We derive very small N/H and N/O ratios for this line of sight that may support a previous suggestion that members of the Sco OB1 association formed from an N-deficient region.Comment: Accepted in The Astrophysical Journal, 9/2006 (expected pub. date: 1/2007) 38 pages, 5 figures (4 color