An introduction to smoothing spline ANOVA models in RKHS, with examples in geographical data, medicine, atmospheric sciences and machine learning

Abstract

This paper is a brief introduction to smoothing spline ANOVA (SS-ANOVA) models in reproducing kernel Hilbert spaces (RKHS) and some of their applications. These models decompose a function of several variables as sums of functions of one variable plus sums of functions of two variables and so forth, analogous to the ordinary analysis of variance decomposition familiar to students in elementary Statistics classes. This is done in such a way that the individual terms are projections onto orthogonal subspaces in RKHS, and the relevant reproducing kernels may be found in many examples. Given the appropriate RKHS, various kinds of estimation and model fitting problems in several variables given observational data can be solved.