Parsimonious Additive Models
A new method for function estimation and variable selection, speciﬁcally designed for additive models ﬁtted by cubic splines is proposed. This new method involves regularizing additive models using the l1-norm, which generalizes the lasso to the nonparametric setting. As in the linear case, it shrinks coefﬁcients and produces some coefﬁcients that are exactly zero. It gives parsimonious models, selects signiﬁcant variables, and reveals nonlinearities in the effects of predictors. Two strategies for ﬁnding a parsimonious additive model solution are proposed. Both algorithms are based on a ﬁxed point algorithm, combined with a singular value decomposition that considerably reduces computation. The empirical behavior of parsimonious additive models is compared to the adaptive backﬁtting BRUTO algorithm. The results allow to characterize the domains in which our approach is effective: it performs signiﬁcantly better than BRUTO when model estimation is challenging. An implementation of this method is illustrated using real data from the Cophar 1 ANRS 102 trial. Parsimonious additive models are applied to predict the indinavir plasma concentration in HIV patients. Results suggest that this new method is a promising technique for the research and application areas.