Efficient Computation of Smoothing Splines via Adaptive Basis Sampling

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Nan Zhang*+ and Ping Ma and Jianhua Z. Huang
• Companies: Texas A&M and University of Georgia and Texas A&M
• Keywords: Nonparametric regression ; Reproducing kernel Hilbert space ; Sampling

Abstract

Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large data sets has hindered their wide applications. We develop a new method named adaptive basis sampling for efficient computation of smoothing splines in super-large samples. A smoothing spline for a regression problem with sample size n can be expressed as a linear combination of n basis functions and its computational complexity is of cubic n. We achieve a more scalable computation by evaluating the smoothing spline using a smaller set of basis functions, which are obtained by an adaptive sampling scheme that utilizes values of the response variable. Our asymptotic analysis shows that smoothing splines computed via adaptive basis sampling converge to the true function at the same rate as the full basis smoothing splines. Using simulation studies and a large scale deep earth core-mantle boundary imaging study, we show that the proposed method outperforms a previous sampling method that does not use the values of response variable.