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Title: Adaptive basis sampling for smoothing splines Authors:  Nan Zhang - Fudan University (China) [presenting]
Abstract: Smoothing splines provide flexible nonparametric regression estimators. However, the high computational cost of smoothing splines for large datasets has hindered their wide application. We develop a new method, named adaptive basis sampling, for efficient computation of smoothing splines in super-large samples. 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 generally of cubic $n$ order. We achieve a more scalable computation in the multivariate case by evaluating the smoothing spline using a smaller set of basis functions, obtained by an adaptive sampling scheme that uses 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 full basis smoothing splines. We show that the proposed method outperforms a sampling method that does not use the values of response variables in several applications.