Divide and Recombine Approaches for Fitting Smoothing Spline Models with Large Datasets
针对大数据集拟合光滑样条模型的计算瓶颈，提出了四种分治与重组方法，通过随机或顺序划分数据并重组结果，在并行计算下实现可扩展性，且性能与全数据方法相当甚至更优。
Spline smoothing is a widely used nonparametric method that allows data to speak for themselves. Due to its complexity and flexibility, fitting smoothing spline models is usually computationally intensive which may become prohibitive with large datasets. To overcome memory and CPU limitations, we propose four divide and recombine (D&R) approaches for fitting cubic splines with large datasets. We consider two approaches to divide the data: random and sequential. For each approach of division, we consider two approaches to recombine. These D&R approaches are implemented in parallel without communication. Extensive simulations show that these D&R approaches are scalable and have comparable performance as the method that uses the whole data. The sequential D&R approaches are spatially adaptive which lead to better performance than the method that uses the whole data when the underlying function is spatially inhomogeneous.