Variable Selection for Global Fréchet Regression

Global Fréchet regression is an extension of linear regression to cover more general types of responses, such as distributions, networks, and manifolds, which are becoming more prevalent. In such models, predictors are Euclidean while responses are metric space valued. Predictor selection is of major relevance for regression modeling in the presence of multiple predictors but has not yet been addressed for Fréchet regression. Due to the metric space-valued nature of the responses, Fréchet regression models do not feature model parameters, and this lack of parameters makes it a major challenge to extend existing variable selection methods for linear regression to global Fréchet regression. In this work, we address this challenge and propose a novel variable selection method that overcomes it and has good practical performance. We provide theoretical support and demonstrate that the proposed variable selection method achieves selection consistency. We also explore the finite sample performance of the proposed method with numerical examples and data illustrations.