Additive models and many smooth univariate functions

Abstract

Additive models build a nonparametric extension of linear models and as such, they exhibit a substantial degree of flexibility. While the most important effects may still be detected by a linear model, substantial improvements are potentially possible by using the more flexible additive model class. At first sight, it seems very ambitious to fit additive models with high-dimensional covariates but sparsity implies feasible computations and good statistical properties. Besides encouraging sparsity, it is important to control smoothness as well. This can be achieved by a sparsity-smoothness penalty function. The combination of sparsity and smoothness is crucial for mathematical theory as well as for better performance on data. We discuss in this chapter methodology and computational aspects which are related to the group Lasso presented in Chapter 4.