Classification by sparse additive models

We consider (nonparametric) sparse 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 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 it is nearly-minimax (up to log-factors) within the entire range of analytic, Sobolev and Besov classes, and illustrate its performance on the real-data example.