The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated within the context of statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel and interpretable way to summarize the relative importance of predictor variables. Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate predictors that are not just marginally important, but whose associations also stem from significant covarying relationships with other variables in the data. We focus on illustrating RATE through Bayesian Gaussian process regression ; although, the methodological innovations apply to other and more general methods. It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for outcomes generated by complex  architectures. With detailed simulations and a botanical QTL mapping study, we show that applying RATE enables an explanation for this improved performance.
The central aim in this paper is to address variable selection questions in nonlinear and nonparametric regression. Motivated by statistical genetics, where nonlinear interactions are of particular interest, we introduce a novel , interpretable, and computationally efficient way to summarize the relative importance of predictor variables. Methodologically, we develop the "RelATive cEntrality" (RATE) measure to prioritize candidate genetic variants that are not just marginally important, but whose associations also stem from significant covarying relationships with other variants in the data. We illustrate RATE through Bayesian Gaussian process regression , but the methodological innovations apply to other nonlinear methods. It is known that nonlinear models often exhibit greater predictive accuracy than linear models, particularly for phenotypes generated by complex genetic architectures. With detailed simulations and an Arabidopsis thaliana QTL mapping study, we show that applying RATE enables an explanation for this improved performance.
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