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.

翻译：本文研究用于分类任务的（非参数）稀疏（广义）加性模型（SpAM）。该SpAM分类器的设计基于最小化逻辑损失函数，同时对单变量加性分量在标准正交级数（如傅里叶级数或小波级数）展开系数施加稀疏群组Lasso/Slope型惩罚。所构建的分类器能天然适应未知的稀疏性与光滑性。我们证明，在特定稀疏群组约束特征值条件下，该分类器在分析类、Sobolev类及Besov类的整个范围内可同时达到近似极小极大最优（仅相差对数因子）。通过模拟数据和真实数据实例验证了所提分类器的性能。