A High-dimensional Additive Nonparametric Model

Abstract

Nonparametric additive models are garnering increasing attention in applied research across fields like statistics and economics, attributed to their distinct interpretability, versatility, and their adeptness at addressing the curse of dimensionality. This paper introduces a novel and efficient fully Bayesian method for estimating nonparametric additive models, employing a band matrix smoothness prior. Our methodology leverages unobserved binary indicator parameters, promoting linearity in each additive component while allowing for deviations from it. We validate the efficacy of our approach through experiments on synthetic data derived from ten-component additive models, encompassing diverse configurations of linear, nonlinear, and zero function components. Additionally, the robustness of our algorithm is tested on high-dimensional models featuring up to one hundred components, and models correlated components. The practical utility and computational efficiency of our technique are further underscored by its application to two real-world datasets, showcasing its broad applicability and effectiveness in various scenarios.