Sure independence screening in ultrahigh dimensional generalized additive models

Generalized additive models (GAMs) have gained popularity by addressing the curse of dimensionality in multivariate nonparametric regressions with non-Gaussian responses, including continuous, binary or count data. In this paper, we propose a fast and efficient feature screening method for GAMs with ultrahigh dimensional covariates. We provide some theoretical justifications for our screening method and establish the sure screening property. We further examine the finite sample performance of the proposed screening procedure and compare it with some existing methods via Monte Carlo simulations. Three real data examples are used to illustrate the effectiveness of the new method.