Classification by sparse generalized additive models
This work addresses classification problems where data have sparse additive structures, offering a theoretically sound and adaptive approach, though it appears incremental as it builds on existing sparse additive modeling techniques.
The paper tackles classification using sparse generalized additive models by minimizing logistic loss with sparse group penalties, achieving near-minimax optimality across analytic, Sobolev, and Besov classes. The method is adaptive to unknown sparsity and smoothness, with performance validated on simulated and real data.
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.