B1202
Title: Uniform design motivated basis selection methods for smoothing spline regression
Authors: Jun Yu - Beijing Institute of Technology (China) [presenting]
Abstract: Fitting a smoothing spline model on a large-scale dataset is daunting due to the high computational cost. The basis selection methods for smoothing spline calculation are regarded as an efficient way to deal with the large-scale dataset. The key to success is to force a non-parametric function in an infinite-dimensional functional space to reside in a relatively small and finite-dimensional model space without the loss of too much prediction accuracy. Space-filling basis selection is proven more efficient among various basis selection methods since the dimension of its model space is smaller than others. Two efficient space-filling basis selection methods are illustrated for smoothing spline calculation. The key idea is to make a uniform design adapt to the large-scale dataset and use projective uniformity to improve the statistical efficiency when the underlying response surface is not isomorphic. It is proved that the illustrated estimator has the same convergence rate as the full-basis estimator. Compared with the standard approach, the proposed method significantly reduces the computational cost.
