  The additive model is a popular nonparametric regression method due to its
ability to retain modeling flexibility while avoiding the curse of
dimensionality. The backfitting algorithm is an intuitive and widely used
numerical approach for fitting additive models. However, its application to
large datasets may incur a high computational cost and is thus infeasible in
practice. To address this problem, we propose a novel approach called
independence-encouraging subsampling (IES) to select a subsample from big data
for training additive models. Inspired by the minimax optimality of an
orthogonal array (OA) due to its pairwise independent predictors and uniform
coverage for the range of each predictor, the IES approach selects a subsample
that approximates an OA to achieve the minimax optimality. Our asymptotic
analyses demonstrate that an IES subsample converges to an OA and that the
backfitting algorithm over the subsample converges to a unique solution even if
the predictors are highly dependent in the original big data. The proposed IES
method is also shown to be numerically appealing via simulations and a real
data application.
