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 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：本文研究了用于分类的非参数稀疏加性模型（SpAM）。该分类器的设计基于最小化逻辑损失，并在单变量加性分量在正交基（如傅里叶级数或小波）展开系数上施加稀疏组Lasso/Slope型惩罚项。所得分类器天然适应未知的稀疏性和光滑性。我们证明，在满足特定稀疏组特征值约束条件下，该分类器在解析类、索伯列夫类及贝索夫类的全体范围内，同时达到近乎极小极大最优（仅含对数因子）。通过模拟算例与真实数据实例验证了所提分类器的性能。