Generalized additive modelling with implicit variable selection by likelihood based boosting

The use of generalized additive models in statistical data analysis
suffers from the restriction to few explanatory variables and the
problems of selection of smoothing parameters. Generalized additive
model boosting circumvents these problems by means of stagewise
fitting of weak learners. A fitting procedure is derived which
works for all simple exponential family distributions, including
binomial, Poisson and normal response variables. The procedure
combines the selection of variables and the determination of the
appropriate amount of smoothing. As weak learners penalized
regression splines and the newly introduced penalized stumps are
considered. Estimates of standard deviations and stopping criteria
which are notorious problems in iterative procedures are based on
an approximate hat matrix. The method is shown to outperform common
procedures for the fitting of generalized additive models. In
particular in high dimensional settings it is the only method that
works properly.