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The central aim in this paper is to address variable selection questions innonlinear and nonparametric regression. Motivated by statistical genetics,where nonlinear interactions are of particular interest, we introduce a noveland interpretable way to summarize the relative importance of predictorvariables. Methodologically, we develop the "RelATive cEntrality" (RATE)measure to prioritize candidate genetic variants that are not just marginallyimportant, but whose associations also stem from significant covaryingrelationships with other variants in the data. We illustrate RATE throughBayesian Gaussian process regression, but the methodological innovations applyto other "black box" methods. It is known that nonlinear models often exhibitgreater predictive accuracy than linear models, particularly for phenotypesgenerated by complex genetic architectures. With detailed simulations and tworeal data association mapping studies, we show that applying RATE enables anexplanation for this improved performance.

Variable Prioritization in Nonlinear Black Box Methods: A Genetic Association Case Study