  We consider (nonparametric) sparse (generalized) additive models (SpAM) for
classification. The design of a SpAM classifier is based on minimizing the
logistic loss with a sparse group Lasso/Slope-type penalties on the
coefficients of univariate additive components' expansions in orthonormal
series (e.g., Fourier or wavelets). The resulting classifier is inherently
adaptive to the unknown sparsity and smoothness. We show that under certain
sparse group restricted eigenvalue condition it is nearly-minimax (up to
log-factors) simultaneously across the entire range of analytic, Sobolev and
Besov classes. The performance of the proposed classifier is illustrated on a
simulated and a real-data examples.
