Scalable Computation of Multivariate Smoothing Splines via Adaptive Basis Sampling

• Activity Number: 181
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Nan Zhang* and Ping Ma and Jianhua Huang
• Companies: Texas A&M University and University of Georgia and Texas A&M University
• Keywords: Nonparametric regression ; Sampling ; Exponential family

Abstract

Smoothing splines via the penalized likelihood method provide effective nonparametric models for regression with responses from exponential families. In general, the computation of smoothing splines is of the order O(n^3), n being the sample size. To achieve a scalable computation for large data sets with multivariate covariates, we develop an adaptive sampling method to select basis functions and construct a low-dimensional approximation of the estimates. Our asymptotic analysis shows such approximation converges to the true function at the same rate as full basis smoothing spline estimator. Empirical results are presented to compare competing methods under multivariate cases.