We 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.
Joint work with Lorin Crawford, Daniel Runcie, Mike West. arXiv draft [Crawford, Flaxman, Runcie, West 2018]:
Seth Flaxman is a lecturer in the statistics section of the Department of Mathematics at Imperial College London, joint with the Data Science Institute. He is also part of the Machine Learning Initiativeat Imperial. His research is on scalable methods and flexible models for spatiotemporal statistics and Bayesian machine learning, applied to public policy and social science. He has worked on application areas that include public health, crime, voting patterns, filter bubbles / echo chambers in media, the regulation of machine learning algorithms, and emotion.