A variable screening procedure via correlation learning was proposed Fan and
Lv (2008) to reduce dimensionality in sparse ultra-high dimensional models.
Even when the true model is linear, the marginal regression can be highly
nonlinear. To address this issue, we further extend the correlation learning to
marginal nonparametric learning. Our nonparametric independence screening is
called NIS, a specific member of the sure independence screening. Several
closely related variable screening procedures are proposed.

Ultrahigh dimensional variable selection plays an increasingly important role
in contemporary scientific discoveries and statistical research. Among others,
Fan and Lv (2008) propose an independent screening framework by ranking the
marginal correlations. They showed that the correlation ranking procedure
possesses a sure independence screening property within the context of the
linear model with Gaussian covariates and responses.