## Dynamic trees can aid in performance tuning of scientific codes

June 10, 2013As heterogeneous computers become more common, researchers are exploring ways to be able to tune scientific applications for the new architectures “just in time.” Two popular approaches that have been used for performance tuning are variable selection and sensitivity analysis. The former focuses on choosing a subset of covariates that should be included in a model, in that they lead to predictions of low variance and high accuracy; the latter seeks to characterize how components of this subset influence the response. Unfortunately, because existing tools are difficult to use, these two approaches typically are treated separately, resulting in inefficiency and increased computational cost.

Researchers from the University of Chicago Booth School of Business, together with Stefan Wild, an assistant computational mathematician in the Mathematics and Computer Science Division at Argonne, have recently demonstrated how the dynamic tree model can support both variable selection and sensitivity analysis of inputs.

By borrowing relevance statistics from classical trees, sensitivity indices from Gaussian process models, and the full probability model characterized by dynamic trees, the research team has produced a data analysis tool that can be used for variable selection, dimension reduction, and visualization of problems several orders of magnitude larger than previously possible. Moreover, the same computational techniques can be used, for example, in regression and classification applications with minimal modification.

The collaborative project was born out of a SQuaREs (Structured Quartet Research Ensembles) program at the American Institute of Mathematics. The purpose of a SQuaRE is to allow a small group of researchers to work for a week or two at the AIM headquarters in Palo Alto, Calif., on a specific topic.

#### Reference

Robert Gramacy, Matthew Taddy, and Stefan Wild, "**Variable Selection and Sensitivity Analysis via Dynamic Trees with an Application to Computer Code Performance Tuning**," *Annals of Applied Statistics* 7(1), 51-80 (2013).